Alfred Tauber (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Alfred Tauber" in English language version.

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The death date is reported in (Sigmund 2004, p. 33) and also in Tauber's VIAF record Archived 2018-09-18 at the Wayback Machine, line 678: Sigmund (2004, pp. 31–33) also gives a description of the events of the last years of Tauber's life, up to the days of his deportation. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036.
(Pinl & Dick 1974, pp. 202–203). Pinl, Maximilian; Dick, Auguste (1974), "Kollegen in einer dunklen Zeit. Schluß", Jahresbericht der Deutschen Mathematiker-Vereinigung (in German), 75: 202–203, MR 0476359, Zbl 0281.01013.
Sigmund (2004, p. 2) states that he was forced to keep holding his course on actuarial mathematics by his low pension. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036.
(Sigmund 2004, p. 21 and p. 28). Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036.
(Fischer et al. 1990, p. 812, footnote 14). Fischer, Gerd; Hirzebruch, Friedrich; Scharlau, Winfried; Törnig, Willi, eds. (1990), Ein Jahrhundert Mathematik 1890 – 1990: Festschrift zum Jubiläum der DMV, Dokumente zur Geschichte der Mathematik (in German), vol. Band 6, Braunschweig / Wiesbaden: Friedrich Vieweg & Sohn, pp. XII+830, doi:10.1007/978-3-322-80265-1, ISBN 3-528-06326-2, MR 1085961, Zbl 0706.01002.
In the exact authors' words, "Unendliche Reihen, Fouriersche Reihen, Kugelfunktionen, Quaternionen,..., Analitische und Darstellende Geometrie" (Pinl & Dick 1974, p. 202). Pinl, Maximilian; Dick, Auguste (1974), "Kollegen in einer dunklen Zeit. Schluß", Jahresbericht der Deutschen Mathematiker-Vereinigung (in German), 75: 202–203, MR 0476359, Zbl 0281.01013.
See for example (Hardy 1949, p. 149), (Hlawka 2007), (Korevaar 2004, p. VII, p. 2 and p. 10), (Lune 1986, p. 2, §1.1 "Tauber's first theorem") and (Sigmund 2004, p. 21). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Hlawka, Edmund (2007), "Tauber, Alfred", Complete Dictionary of Scientific Biography, New York: Charles Scribner's Sons, retrieved 27 February 2016. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036.
See for example (Hardy 1949, p. 149) and (Korevaar 2004, p. 6). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002.
See (Hardy 1949, p. 149), (Hlawka 2007) and (Lune 1986, p. 2 §1.1 "Tauber's first theorem"). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Hlawka, Edmund (2007), "Tauber, Alfred", Complete Dictionary of Scientific Biography, New York: Charles Scribner's Sons, retrieved 27 February 2016. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.
See (Korevaar 2004, p. 2) and (Sigmund 2004, p. 21): Korevaar precises that the locution "Tauberian theorems" was first used in the short note (Hardy & Littlewood 1913). Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036. Hardy, G. H.; Littlewood, J. E. (1913), "Tauberian theorems concerning series of positive terms", Messenger of Mathematics, XLII: 191–192, JFM 44.0283.01.
See (Hardy 1949, p. 149 and p. 150), (Korevaar 2004, p. 10 and p. 11) and (Lune 1986, p. 2, §1.1 "Tauber's first theorem" and p. 4, §1.1 "Tauber's second theorem"). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.
See for example (Hardy 1949, p. 149), (Korevaar 2004, p. 10) and (Lune 1986, p. 2, §1.1 "Tauber's first theorem"). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.
See also (Lune 1986, p. 2, §1.1 "Tauber's first theorem") and (Hardy 1949, p. 149): Sigmund (2004, p. 21) incorrectly attributes this role to Tauber's second theorem. See also the analysis by Chatterji (1984, pp. 169–170 and p. 172). Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002. Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036. Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005.
See (Hardy 1949, p. 149), Chatterji (1984, p. 169 and p. 172) and (Korevaar 2004, p. 6). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002.
See (Chatterji 1984, p. 169 theorem B), (Lune 1986, p. 4, §1.2 "Tauber's second theorem") and the remark by Korevaar (2004, p. 11): Hardy (1949, pp. 150–152) proves this theorem by proving a more general one involving Riemann–Stieltjes integrals. Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341.
(Chatterji 1984, p. 169 theorem A), (Korevaar 2004, p. 11). Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002.
See for example (Hardy 1949, p. 150), (Korevaar 2004, p. 11) and (Lune 1986, p. 4, §1.2 "Tauber's second theorem"). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.
According to Chatterji (1984, p. 172): see also the proofs of the two theorems given by Lune (1986, chapter 1, §§1.1–1.2, pp. 2–7). Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.
In King's words (2009, p.3), "In hindsight, perhaps the transform should bear the names of the three aforementioned authors". King, Frederick W. (2009), Hilbert transforms. Volume 1, Encyclopedia of Mathematics and its Applications, vol. 124, Cambridge: Cambridge University Press, pp. xxxviii+858, ISBN 978-0-521-88762-5, MR 2542214, Zbl 1188.44005.
The analysis presented closely follows (King 2009, p. 131), which in turn follows (Tauber 1891, pp. 79–80). King, Frederick W. (2009), Hilbert transforms. Volume 1, Encyclopedia of Mathematics and its Applications, vol. 124, Cambridge: Cambridge University Press, pp. xxxviii+858, ISBN 978-0-521-88762-5, MR 2542214, Zbl 1188.44005.
As King (2009, p. 131) notes, this non-standard definition of the real and imaginary part of the $k$ th complex coefficient of a power series is purposefully introduced in order to hidden ("suppress") the functional dependence of $φ$ and $ψ$ on $r$ . King, Frederick W. (2009), Hilbert transforms. Volume 1, Encyclopedia of Mathematics and its Applications, vol. 124, Cambridge: Cambridge University Press, pp. xxxviii+858, ISBN 978-0-521-88762-5, MR 2542214, Zbl 1188.44005.
(King 2009, p. 131). King, Frederick W. (2009), Hilbert transforms. Volume 1, Encyclopedia of Mathematics and its Applications, vol. 124, Cambridge: Cambridge University Press, pp. xxxviii+858, ISBN 978-0-521-88762-5, MR 2542214, Zbl 1188.44005.

ams.org

The 2010 Mathematics Subject Classification has two entries on Tauberian theorems: the entry 11M45, belonging to the "Number theory" area, and the entry 40E05, belonging to the "Sequences, series, summability" area.

books.google.com

(Fischer et al. 1990, p. 812, footnote 14). Fischer, Gerd; Hirzebruch, Friedrich; Scharlau, Winfried; Törnig, Willi, eds. (1990), Ein Jahrhundert Mathematik 1890 – 1990: Festschrift zum Jubiläum der DMV, Dokumente zur Geschichte der Mathematik (in German), vol. Band 6, Braunschweig / Wiesbaden: Friedrich Vieweg & Sohn, pp. XII+830, doi:10.1007/978-3-322-80265-1, ISBN 3-528-06326-2, MR 1085961, Zbl 0706.01002.
See also (Lune 1986, p. 2, §1.1 "Tauber's first theorem") and (Hardy 1949, p. 149): Sigmund (2004, p. 21) incorrectly attributes this role to Tauber's second theorem. See also the analysis by Chatterji (1984, pp. 169–170 and p. 172). Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002. Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036. Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005.
See (Hardy 1949, p. 149), Chatterji (1984, p. 169 and p. 172) and (Korevaar 2004, p. 6). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002.
See (Chatterji 1984, p. 169 theorem B), (Lune 1986, p. 4, §1.2 "Tauber's second theorem") and the remark by Korevaar (2004, p. 11): Hardy (1949, pp. 150–152) proves this theorem by proving a more general one involving Riemann–Stieltjes integrals. Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341.
(Chatterji 1984, p. 169 theorem A), (Korevaar 2004, p. 11). Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002.
According to Chatterji (1984, p. 172): see also the proofs of the two theorems given by Lune (1986, chapter 1, §§1.1–1.2, pp. 2–7). Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.
Again according to Chatterji (1984, p. 172). Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005.

doi.org

The death date is reported in (Sigmund 2004, p. 33) and also in Tauber's VIAF record Archived 2018-09-18 at the Wayback Machine, line 678: Sigmund (2004, pp. 31–33) also gives a description of the events of the last years of Tauber's life, up to the days of his deportation. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036.
Sigmund (2004, p. 2) states that he was forced to keep holding his course on actuarial mathematics by his low pension. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036.
(Sigmund 2004, p. 21 and p. 28). Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036.
(Fischer et al. 1990, p. 812, footnote 14). Fischer, Gerd; Hirzebruch, Friedrich; Scharlau, Winfried; Törnig, Willi, eds. (1990), Ein Jahrhundert Mathematik 1890 – 1990: Festschrift zum Jubiläum der DMV, Dokumente zur Geschichte der Mathematik (in German), vol. Band 6, Braunschweig / Wiesbaden: Friedrich Vieweg & Sohn, pp. XII+830, doi:10.1007/978-3-322-80265-1, ISBN 3-528-06326-2, MR 1085961, Zbl 0706.01002.
See for example (Hardy 1949, p. 149), (Hlawka 2007), (Korevaar 2004, p. VII, p. 2 and p. 10), (Lune 1986, p. 2, §1.1 "Tauber's first theorem") and (Sigmund 2004, p. 21). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Hlawka, Edmund (2007), "Tauber, Alfred", Complete Dictionary of Scientific Biography, New York: Charles Scribner's Sons, retrieved 27 February 2016. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036.
See for example (Hardy 1949, p. 149) and (Korevaar 2004, p. 6). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002.
See (Korevaar 2004, p. 2) and (Sigmund 2004, p. 21): Korevaar precises that the locution "Tauberian theorems" was first used in the short note (Hardy & Littlewood 1913). Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036. Hardy, G. H.; Littlewood, J. E. (1913), "Tauberian theorems concerning series of positive terms", Messenger of Mathematics, XLII: 191–192, JFM 44.0283.01.
See (Hardy 1949, p. 149 and p. 150), (Korevaar 2004, p. 10 and p. 11) and (Lune 1986, p. 2, §1.1 "Tauber's first theorem" and p. 4, §1.1 "Tauber's second theorem"). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.
See for example (Hardy 1949, p. 149), (Korevaar 2004, p. 10) and (Lune 1986, p. 2, §1.1 "Tauber's first theorem"). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.
See also (Lune 1986, p. 2, §1.1 "Tauber's first theorem") and (Hardy 1949, p. 149): Sigmund (2004, p. 21) incorrectly attributes this role to Tauber's second theorem. See also the analysis by Chatterji (1984, pp. 169–170 and p. 172). Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002. Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036. Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005.
See (Hardy 1949, p. 149), Chatterji (1984, p. 169 and p. 172) and (Korevaar 2004, p. 6). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002.
See (Chatterji 1984, p. 169 theorem B), (Lune 1986, p. 4, §1.2 "Tauber's second theorem") and the remark by Korevaar (2004, p. 11): Hardy (1949, pp. 150–152) proves this theorem by proving a more general one involving Riemann–Stieltjes integrals. Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341.
(Chatterji 1984, p. 169 theorem A), (Korevaar 2004, p. 11). Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002.
See for example (Hardy 1949, p. 150), (Korevaar 2004, p. 11) and (Lune 1986, p. 4, §1.2 "Tauber's second theorem"). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.

emis.de

See the results of Jahrbuch query: "au = (TAUBER, A*)".

encyclopedia.com

(Hlawka 2007). Hlawka, Edmund (2007), "Tauber, Alfred", Complete Dictionary of Scientific Biography, New York: Charles Scribner's Sons, retrieved 27 February 2016.
According to Hlawka (2007), he wrote his doctoral dissertation in 1888. Hlawka, Edmund (2007), "Tauber, Alfred", Complete Dictionary of Scientific Biography, New York: Charles Scribner's Sons, retrieved 27 February 2016.
According to Hlawka's classification (2007). Hlawka, Edmund (2007), "Tauber, Alfred", Complete Dictionary of Scientific Biography, New York: Charles Scribner's Sons, retrieved 27 February 2016.
See for example (Hardy 1949, p. 149), (Hlawka 2007), (Korevaar 2004, p. VII, p. 2 and p. 10), (Lune 1986, p. 2, §1.1 "Tauber's first theorem") and (Sigmund 2004, p. 21). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Hlawka, Edmund (2007), "Tauber, Alfred", Complete Dictionary of Scientific Biography, New York: Charles Scribner's Sons, retrieved 27 February 2016. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036.
See (Hardy 1949, p. 149), (Hlawka 2007) and (Lune 1986, p. 2 §1.1 "Tauber's first theorem"). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Hlawka, Edmund (2007), "Tauber, Alfred", Complete Dictionary of Scientific Biography, New York: Charles Scribner's Sons, retrieved 27 February 2016. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.

eudml.org

(Pinl & Dick 1974, pp. 202–203). Pinl, Maximilian; Dick, Auguste (1974), "Kollegen in einer dunklen Zeit. Schluß", Jahresbericht der Deutschen Mathematiker-Vereinigung (in German), 75: 202–203, MR 0476359, Zbl 0281.01013.
In the exact authors' words, "Unendliche Reihen, Fouriersche Reihen, Kugelfunktionen, Quaternionen,..., Analitische und Darstellende Geometrie" (Pinl & Dick 1974, p. 202). Pinl, Maximilian; Dick, Auguste (1974), "Kollegen in einer dunklen Zeit. Schluß", Jahresbericht der Deutschen Mathematiker-Vereinigung (in German), 75: 202–203, MR 0476359, Zbl 0281.01013.

loc.gov

lccn.loc.gov

See for example (Hardy 1949, p. 149), (Hlawka 2007), (Korevaar 2004, p. VII, p. 2 and p. 10), (Lune 1986, p. 2, §1.1 "Tauber's first theorem") and (Sigmund 2004, p. 21). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Hlawka, Edmund (2007), "Tauber, Alfred", Complete Dictionary of Scientific Biography, New York: Charles Scribner's Sons, retrieved 27 February 2016. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036.
See for example (Hardy 1949, p. 149) and (Korevaar 2004, p. 6). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002.
See (Hardy 1949, p. 149), (Hlawka 2007) and (Lune 1986, p. 2 §1.1 "Tauber's first theorem"). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Hlawka, Edmund (2007), "Tauber, Alfred", Complete Dictionary of Scientific Biography, New York: Charles Scribner's Sons, retrieved 27 February 2016. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.
See (Hardy 1949, p. 149 and p. 150), (Korevaar 2004, p. 10 and p. 11) and (Lune 1986, p. 2, §1.1 "Tauber's first theorem" and p. 4, §1.1 "Tauber's second theorem"). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.
See for example (Hardy 1949, p. 149), (Korevaar 2004, p. 10) and (Lune 1986, p. 2, §1.1 "Tauber's first theorem"). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.
See also (Lune 1986, p. 2, §1.1 "Tauber's first theorem") and (Hardy 1949, p. 149): Sigmund (2004, p. 21) incorrectly attributes this role to Tauber's second theorem. See also the analysis by Chatterji (1984, pp. 169–170 and p. 172). Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002. Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036. Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005.
See (Hardy 1949, p. 149), Chatterji (1984, p. 169 and p. 172) and (Korevaar 2004, p. 6). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002.
See (Chatterji 1984, p. 169 theorem B), (Lune 1986, p. 4, §1.2 "Tauber's second theorem") and the remark by Korevaar (2004, p. 11): Hardy (1949, pp. 150–152) proves this theorem by proving a more general one involving Riemann–Stieltjes integrals. Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341.
See for example (Hardy 1949, p. 150), (Korevaar 2004, p. 11) and (Lune 1986, p. 4, §1.2 "Tauber's second theorem"). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.

loc.gov

See for example (Hardy 1949, p. 149), (Hlawka 2007), (Korevaar 2004, p. VII, p. 2 and p. 10), (Lune 1986, p. 2, §1.1 "Tauber's first theorem") and (Sigmund 2004, p. 21). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Hlawka, Edmund (2007), "Tauber, Alfred", Complete Dictionary of Scientific Biography, New York: Charles Scribner's Sons, retrieved 27 February 2016. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036.
See for example (Hardy 1949, p. 149) and (Korevaar 2004, p. 6). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002.
See (Hardy 1949, p. 149), (Hlawka 2007) and (Lune 1986, p. 2 §1.1 "Tauber's first theorem"). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Hlawka, Edmund (2007), "Tauber, Alfred", Complete Dictionary of Scientific Biography, New York: Charles Scribner's Sons, retrieved 27 February 2016. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.
See (Hardy 1949, p. 149 and p. 150), (Korevaar 2004, p. 10 and p. 11) and (Lune 1986, p. 2, §1.1 "Tauber's first theorem" and p. 4, §1.1 "Tauber's second theorem"). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.
See for example (Hardy 1949, p. 149), (Korevaar 2004, p. 10) and (Lune 1986, p. 2, §1.1 "Tauber's first theorem"). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.
See also (Lune 1986, p. 2, §1.1 "Tauber's first theorem") and (Hardy 1949, p. 149): Sigmund (2004, p. 21) incorrectly attributes this role to Tauber's second theorem. See also the analysis by Chatterji (1984, pp. 169–170 and p. 172). Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002. Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036. Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005.
See (Hardy 1949, p. 149), Chatterji (1984, p. 169 and p. 172) and (Korevaar 2004, p. 6). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002.
See (Chatterji 1984, p. 169 theorem B), (Lune 1986, p. 4, §1.2 "Tauber's second theorem") and the remark by Korevaar (2004, p. 11): Hardy (1949, pp. 150–152) proves this theorem by proving a more general one involving Riemann–Stieltjes integrals. Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341.
See for example (Hardy 1949, p. 150), (Korevaar 2004, p. 11) and (Lune 1986, p. 4, §1.2 "Tauber's second theorem"). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.

persistent-identifier.org

See for example (Hardy 1949, p. 149), (Hlawka 2007), (Korevaar 2004, p. VII, p. 2 and p. 10), (Lune 1986, p. 2, §1.1 "Tauber's first theorem") and (Sigmund 2004, p. 21). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Hlawka, Edmund (2007), "Tauber, Alfred", Complete Dictionary of Scientific Biography, New York: Charles Scribner's Sons, retrieved 27 February 2016. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036.
See (Hardy 1949, p. 149), (Hlawka 2007) and (Lune 1986, p. 2 §1.1 "Tauber's first theorem"). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Hlawka, Edmund (2007), "Tauber, Alfred", Complete Dictionary of Scientific Biography, New York: Charles Scribner's Sons, retrieved 27 February 2016. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.
See (Hardy 1949, p. 149 and p. 150), (Korevaar 2004, p. 10 and p. 11) and (Lune 1986, p. 2, §1.1 "Tauber's first theorem" and p. 4, §1.1 "Tauber's second theorem"). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.
See for example (Hardy 1949, p. 149), (Korevaar 2004, p. 10) and (Lune 1986, p. 2, §1.1 "Tauber's first theorem"). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.
See also (Lune 1986, p. 2, §1.1 "Tauber's first theorem") and (Hardy 1949, p. 149): Sigmund (2004, p. 21) incorrectly attributes this role to Tauber's second theorem. See also the analysis by Chatterji (1984, pp. 169–170 and p. 172). Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002. Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036. Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005.
See (Chatterji 1984, p. 169 theorem B), (Lune 1986, p. 4, §1.2 "Tauber's second theorem") and the remark by Korevaar (2004, p. 11): Hardy (1949, pp. 150–152) proves this theorem by proving a more general one involving Riemann–Stieltjes integrals. Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341.
See for example (Hardy 1949, p. 150), (Korevaar 2004, p. 11) and (Lune 1986, p. 4, §1.2 "Tauber's second theorem"). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.
According to Chatterji (1984, p. 172): see also the proofs of the two theorems given by Lune (1986, chapter 1, §§1.1–1.2, pp. 2–7). Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.

semanticscholar.org

api.semanticscholar.org

The death date is reported in (Sigmund 2004, p. 33) and also in Tauber's VIAF record Archived 2018-09-18 at the Wayback Machine, line 678: Sigmund (2004, pp. 31–33) also gives a description of the events of the last years of Tauber's life, up to the days of his deportation. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036.
Sigmund (2004, p. 2) states that he was forced to keep holding his course on actuarial mathematics by his low pension. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036.
(Sigmund 2004, p. 21 and p. 28). Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036.
See for example (Hardy 1949, p. 149), (Hlawka 2007), (Korevaar 2004, p. VII, p. 2 and p. 10), (Lune 1986, p. 2, §1.1 "Tauber's first theorem") and (Sigmund 2004, p. 21). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Hlawka, Edmund (2007), "Tauber, Alfred", Complete Dictionary of Scientific Biography, New York: Charles Scribner's Sons, retrieved 27 February 2016. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036.
See (Korevaar 2004, p. 2) and (Sigmund 2004, p. 21): Korevaar precises that the locution "Tauberian theorems" was first used in the short note (Hardy & Littlewood 1913). Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036. Hardy, G. H.; Littlewood, J. E. (1913), "Tauberian theorems concerning series of positive terms", Messenger of Mathematics, XLII: 191–192, JFM 44.0283.01.
See also (Lune 1986, p. 2, §1.1 "Tauber's first theorem") and (Hardy 1949, p. 149): Sigmund (2004, p. 21) incorrectly attributes this role to Tauber's second theorem. See also the analysis by Chatterji (1984, pp. 169–170 and p. 172). Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002. Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036. Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005.

uni-goettingen.de

gdz.sub.uni-goettingen.de

See also the short research announce (Tauber 1895). Tauber, Alfred (1895), "Ueber die Werte einer analytischen Function längs einer Kreislinie" [On the values of an analytic function along a circular perimeter], Jahresbericht der Deutschen Mathematiker-Vereinigung, 4: 115, archived from the original on 2015-07-01, retrieved 2014-07-16.

viaf.org

The death date is reported in (Sigmund 2004, p. 33) and also in Tauber's VIAF record Archived 2018-09-18 at the Wayback Machine, line 678: Sigmund (2004, pp. 31–33) also gives a description of the events of the last years of Tauber's life, up to the days of his deportation. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036.

web.archive.org

The death date is reported in (Sigmund 2004, p. 33) and also in Tauber's VIAF record Archived 2018-09-18 at the Wayback Machine, line 678: Sigmund (2004, pp. 31–33) also gives a description of the events of the last years of Tauber's life, up to the days of his deportation. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036.
See also the short research announce (Tauber 1895). Tauber, Alfred (1895), "Ueber die Werte einer analytischen Function längs einer Kreislinie" [On the values of an analytic function along a circular perimeter], Jahresbericht der Deutschen Mathematiker-Vereinigung, 4: 115, archived from the original on 2015-07-01, retrieved 2014-07-16.

worldcat.org

See for example (Hardy 1949, p. 149), (Hlawka 2007), (Korevaar 2004, p. VII, p. 2 and p. 10), (Lune 1986, p. 2, §1.1 "Tauber's first theorem") and (Sigmund 2004, p. 21). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Hlawka, Edmund (2007), "Tauber, Alfred", Complete Dictionary of Scientific Biography, New York: Charles Scribner's Sons, retrieved 27 February 2016. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036.
See for example (Hardy 1949, p. 149) and (Korevaar 2004, p. 6). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002.
See (Hardy 1949, p. 149), (Hlawka 2007) and (Lune 1986, p. 2 §1.1 "Tauber's first theorem"). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Hlawka, Edmund (2007), "Tauber, Alfred", Complete Dictionary of Scientific Biography, New York: Charles Scribner's Sons, retrieved 27 February 2016. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.
See (Hardy 1949, p. 149 and p. 150), (Korevaar 2004, p. 10 and p. 11) and (Lune 1986, p. 2, §1.1 "Tauber's first theorem" and p. 4, §1.1 "Tauber's second theorem"). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.
See for example (Hardy 1949, p. 149), (Korevaar 2004, p. 10) and (Lune 1986, p. 2, §1.1 "Tauber's first theorem"). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.
See also (Lune 1986, p. 2, §1.1 "Tauber's first theorem") and (Hardy 1949, p. 149): Sigmund (2004, p. 21) incorrectly attributes this role to Tauber's second theorem. See also the analysis by Chatterji (1984, pp. 169–170 and p. 172). Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002. Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036. Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005.
See (Hardy 1949, p. 149), Chatterji (1984, p. 169 and p. 172) and (Korevaar 2004, p. 6). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002.
See (Chatterji 1984, p. 169 theorem B), (Lune 1986, p. 4, §1.2 "Tauber's second theorem") and the remark by Korevaar (2004, p. 11): Hardy (1949, pp. 150–152) proves this theorem by proving a more general one involving Riemann–Stieltjes integrals. Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341.
See for example (Hardy 1949, p. 150), (Korevaar 2004, p. 11) and (Lune 1986, p. 4, §1.2 "Tauber's second theorem"). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.

zbmath.org

The death date is reported in (Sigmund 2004, p. 33) and also in Tauber's VIAF record Archived 2018-09-18 at the Wayback Machine, line 678: Sigmund (2004, pp. 31–33) also gives a description of the events of the last years of Tauber's life, up to the days of his deportation. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036.
(Pinl & Dick 1974, pp. 202–203). Pinl, Maximilian; Dick, Auguste (1974), "Kollegen in einer dunklen Zeit. Schluß", Jahresbericht der Deutschen Mathematiker-Vereinigung (in German), 75: 202–203, MR 0476359, Zbl 0281.01013.
Sigmund (2004, p. 2) states that he was forced to keep holding his course on actuarial mathematics by his low pension. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036.
(Sigmund 2004, p. 21 and p. 28). Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036.
(Fischer et al. 1990, p. 812, footnote 14). Fischer, Gerd; Hirzebruch, Friedrich; Scharlau, Winfried; Törnig, Willi, eds. (1990), Ein Jahrhundert Mathematik 1890 – 1990: Festschrift zum Jubiläum der DMV, Dokumente zur Geschichte der Mathematik (in German), vol. Band 6, Braunschweig / Wiesbaden: Friedrich Vieweg & Sohn, pp. XII+830, doi:10.1007/978-3-322-80265-1, ISBN 3-528-06326-2, MR 1085961, Zbl 0706.01002.
In the exact authors' words, "Unendliche Reihen, Fouriersche Reihen, Kugelfunktionen, Quaternionen,..., Analitische und Darstellende Geometrie" (Pinl & Dick 1974, p. 202). Pinl, Maximilian; Dick, Auguste (1974), "Kollegen in einer dunklen Zeit. Schluß", Jahresbericht der Deutschen Mathematiker-Vereinigung (in German), 75: 202–203, MR 0476359, Zbl 0281.01013.
See for example (Hardy 1949, p. 149), (Hlawka 2007), (Korevaar 2004, p. VII, p. 2 and p. 10), (Lune 1986, p. 2, §1.1 "Tauber's first theorem") and (Sigmund 2004, p. 21). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Hlawka, Edmund (2007), "Tauber, Alfred", Complete Dictionary of Scientific Biography, New York: Charles Scribner's Sons, retrieved 27 February 2016. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036.
See for example (Hardy 1949, p. 149) and (Korevaar 2004, p. 6). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002.
See (Hardy 1949, p. 149), (Hlawka 2007) and (Lune 1986, p. 2 §1.1 "Tauber's first theorem"). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Hlawka, Edmund (2007), "Tauber, Alfred", Complete Dictionary of Scientific Biography, New York: Charles Scribner's Sons, retrieved 27 February 2016. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.
See (Korevaar 2004, p. 2) and (Sigmund 2004, p. 21): Korevaar precises that the locution "Tauberian theorems" was first used in the short note (Hardy & Littlewood 1913). Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036. Hardy, G. H.; Littlewood, J. E. (1913), "Tauberian theorems concerning series of positive terms", Messenger of Mathematics, XLII: 191–192, JFM 44.0283.01.
See (Hardy 1949, p. 149 and p. 150), (Korevaar 2004, p. 10 and p. 11) and (Lune 1986, p. 2, §1.1 "Tauber's first theorem" and p. 4, §1.1 "Tauber's second theorem"). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.
See for example (Hardy 1949, p. 149), (Korevaar 2004, p. 10) and (Lune 1986, p. 2, §1.1 "Tauber's first theorem"). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.
See also (Lune 1986, p. 2, §1.1 "Tauber's first theorem") and (Hardy 1949, p. 149): Sigmund (2004, p. 21) incorrectly attributes this role to Tauber's second theorem. See also the analysis by Chatterji (1984, pp. 169–170 and p. 172). Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002. Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Sigmund, Karl (2004), "Failing Phoenix: Tauber, Helly, and Viennese life insurance", The Mathematical Intelligencer, 26 (2): 21–33, doi:10.1007/bf02985648, MR 2067894, S2CID 121108996, Zbl 0849.01036. Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005.
See (Hardy 1949, p. 149), Chatterji (1984, p. 169 and p. 172) and (Korevaar 2004, p. 6). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002.
See (Chatterji 1984, p. 169 theorem B), (Lune 1986, p. 4, §1.2 "Tauber's second theorem") and the remark by Korevaar (2004, p. 11): Hardy (1949, pp. 150–152) proves this theorem by proving a more general one involving Riemann–Stieltjes integrals. Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341.
(Chatterji 1984, p. 169 theorem A), (Korevaar 2004, p. 11). Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002.
See for example (Hardy 1949, p. 150), (Korevaar 2004, p. 11) and (Lune 1986, p. 4, §1.2 "Tauber's second theorem"). Hardy, G. H. (1949), Divergent Series, Oxford: Clarendon Press, xvi+396, ISBN 978-0-8218-2649-2, LCCN 49005496, MR 0030620, OCLC 808787, 2nd Edition published by Chelsea Publishing Company, 1991, LCCN 91-75377, ISBN 0828403341. Korevaar, Jacob (2004), Tauberian theory. A century of developments, Grundlehren der Mathematischen Wissenschaften, vol. 329, Springer-Verlag, pp. xvi+483, doi:10.1007/978-3-662-10225-1, ISBN 3-540-21058-X, MR 2073637, Zbl 1056.40002. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.
According to Chatterji (1984, p. 172): see also the proofs of the two theorems given by Lune (1986, chapter 1, §§1.1–1.2, pp. 2–7). Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005. Lune, J. van de (1986), An introduction to Tauberian theory: from Tauber to Wiener, CWI Syllabus, vol. 12, Amsterdam: CWI, pp. iv+102, ISBN 90-6196-309-5, MR 0882005, Zbl 0636.40002.
Again according to Chatterji (1984, p. 172). Chatterji, S. D. (1984), "Tauber's theorem – a few historical remarks", in Chatterji, S. D. (ed.), Jahrbuch Überblicke Mathematik, Mathematical surveys, vol. 17, Mannheim: Bibliographisches Institut AG, pp. 167–175, Zbl 0555.40008, and also Zbl 0556.01005.
In King's words (2009, p.3), "In hindsight, perhaps the transform should bear the names of the three aforementioned authors". King, Frederick W. (2009), Hilbert transforms. Volume 1, Encyclopedia of Mathematics and its Applications, vol. 124, Cambridge: Cambridge University Press, pp. xxxviii+858, ISBN 978-0-521-88762-5, MR 2542214, Zbl 1188.44005.
The analysis presented closely follows (King 2009, p. 131), which in turn follows (Tauber 1891, pp. 79–80). King, Frederick W. (2009), Hilbert transforms. Volume 1, Encyclopedia of Mathematics and its Applications, vol. 124, Cambridge: Cambridge University Press, pp. xxxviii+858, ISBN 978-0-521-88762-5, MR 2542214, Zbl 1188.44005.
As King (2009, p. 131) notes, this non-standard definition of the real and imaginary part of the $k$ th complex coefficient of a power series is purposefully introduced in order to hidden ("suppress") the functional dependence of $φ$ and $ψ$ on $r$ . King, Frederick W. (2009), Hilbert transforms. Volume 1, Encyclopedia of Mathematics and its Applications, vol. 124, Cambridge: Cambridge University Press, pp. xxxviii+858, ISBN 978-0-521-88762-5, MR 2542214, Zbl 1188.44005.
(King 2009, p. 131). King, Frederick W. (2009), Hilbert transforms. Volume 1, Encyclopedia of Mathematics and its Applications, vol. 124, Cambridge: Cambridge University Press, pp. xxxviii+858, ISBN 978-0-521-88762-5, MR 2542214, Zbl 1188.44005.