Function of several complex variables (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Function of several complex variables" in English language version.

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Siu, Yum-Tong (1978). "Pseudoconvexity and the problem of Levi". Bulletin of the American Mathematical Society. 84 (4): 481–513. doi:10.1090/S0002-9904-1978-14483-8. MR 0477104.
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Serre, Jean-Pierre (1956). "Géométrie algébrique et géométrie analytique". Annales de l'Institut Fourier (in French). 6: 1–42. doi:10.5802/aif.59. ISSN 0373-0956. MR 0082175. Zbl 0075.30401.
Cartan, Henri (1953). "Variétés analytiques complexes et cohomologie". Colloque sur les fonctions de plusieurs variables, Bruxelles: 41–55. MR 0064154. Zbl 0053.05301.
Serre, Jean-Pierre (1955), "Faisceaux algébriques cohérents" (PDF), Annals of Mathematics, 61 (2): 197–278, doi:10.2307/1969915, JSTOR 1969915, MR 0068874
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Hartshorne, Robin (1977). Algebraic Geometry. Graduate Texts in Mathematics. Vol. 52. Berlin, New York: Springer-Verlag. doi:10.1007/978-1-4757-3849-0. ISBN 978-0-387-90244-9. MR 0463157. S2CID 197660097. Zbl 0367.14001.
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archive.org

Hartogs, Fritz (1906), "Einige Folgerungen aus der Cauchyschen Integralformel bei Funktionen mehrerer Veränderlichen.", Sitzungsberichte der Königlich Bayerischen Akademie der Wissenschaften zu München, Mathematisch-Physikalische Klasse (in German), 36: 223–242, JFM 37.0443.01
Weyl, Hermann (2009) [1913], The concept of a Riemann surface (3rd ed.), New York: Dover Publications, ISBN 978-0-486-47004-7, MR 0069903

arxiv.org

Simonič, Aleksander (2016). "Elementary approach to the Hartogs extension theorem". arXiv:1608.00950 [math.CV].
Merker, Joël; Porten, Egmont (2007). "A Morse-theoretical proof of the Hartogs extension theorem". Journal of Geometric Analysis. 17 (3): 513–546. arXiv:math/0610985. doi:10.1007/BF02922095. S2CID 449210.
Huckleberry, Alan (2013). "Hans Grauert (1930–2011)". Jahresbericht der Deutschen Mathematiker-Vereinigung. 115: 21–45. arXiv:1303.6933. doi:10.1365/s13291-013-0061-7. S2CID 119685542.
Noguchi, Junjiro (2019). "A brief chronicle of the Levi (Hartog's inverse) problem, coherence and open problem". Notices of the International Congress of Chinese Mathematicians. 7 (2): 19–24. arXiv:1807.08246. doi:10.4310/ICCM.2019.V7.N2.A2. S2CID 119619733.
Noguchi, Junjiro (2019), "A Weak Coherence Theorem and Remarks to the Oka Theory" (PDF), Kodai Math. J., 42 (3): 566–586, arXiv:1704.07726, doi:10.2996/kmj/1572487232, S2CID 119697608
Fornaess, J.E.; Forstneric, F; Wold, E.F (2020). "The Legacy of Weierstrass, Runge, Oka–Weil, and Mergelyan". In Breaz, Daniel; Rassias, Michael Th. (eds.). Advancements in Complex Analysis – Holomorphic Approximation. Springer Nature. pp. 133–192. arXiv:1802.03924. doi:10.1007/978-3-030-40120-7. ISBN 978-3-030-40119-1. S2CID 220266044.
Patyi, Imre (2011). "On complex Banach manifolds similar to Stein manifolds". Comptes Rendus Mathematique. 349 (1–2): 43–45. arXiv:1010.3738. doi:10.1016/j.crma.2010.11.020. S2CID 119631664.
Noguchi, Junjiro (2011). "Another Direct Proof of Oka's Theorem (Oka IX)" (PDF). J. Math. Sci. Univ. Tokyo. 19 (4). arXiv:1108.2078. MR 3086750.
Sibony, Nessim (2018). "Levi problem in complex manifolds". Mathematische Annalen. 371 (3–4): 1047–1067. arXiv:1610.07768. doi:10.1007/s00208-017-1539-x. S2CID 119670805.
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bnf.fr

gallica.bnf.fr

Remmert, Reinhold (1956). "Sur les espaces analytiques holomorphiquement séparables et holomorphiquement convexes". Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences de Paris (in French). 243: 118–121. Zbl 0070.30401.
Cartan, Henri; Serre, Jean-Pierre (1953). "Un théorème de finitude concernant les variétés analytiques compactes". Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences de Paris. 237: 128–130. Zbl 0050.17701.

books.google.com

Ohsawa, Takeo (2002). Analysis of Several Complex Variables. ISBN 978-1-4704-4636-9.
Siu, Yum-Tong (1991). "Uniformization in Several Complex Variables". In Wu, Hung-Hsi (ed.). Contemporary Geometry. p. 494. doi:10.1007/978-1-4684-7950-8. ISBN 978-1-4684-7950-8.
Jarnicki, Marek; Pflug, Peter (2008). First Steps in Several Complex Variables: Reinhardt Domains. doi:10.4171/049. ISBN 978-3-03719-049-4.
Range, R. Michael (1986). "Domains of Holomorphy and Pseudoconvexity". Holomorphic Functions and Integral Representations in Several Complex Variables. Graduate Texts in Mathematics. Vol. 108. p. 10.1007/978-1-4757-1918-5_2. doi:10.1007/978-1-4757-1918-5_2. ISBN 978-1-4419-3078-1.
Sheaves on Manifolds. Grundlehren der mathematischen Wissenschaften. Vol. 136. 1990. doi:10.1007/978-3-662-02661-8. ISBN 978-3-642-08082-1.
Serre, Jean-Pierre (1953). "Quelques problèmes globaux rélatifs aux variétés de Stein". Centre Belge Rech. Math., Colloque Fonctions Plusieurs Variables, Bruxelles du 11 Au 14 Mars: 67–58. Zbl 0053.05302.
Forstnerič, Franc (2011). "Stein Manifolds". Stein Manifolds and Holomorphic Mappings. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics. Vol. 56. doi:10.1007/978-3-642-22250-4. ISBN 978-3-642-22249-8.
Fritzsche, Klaus; Grauert, Hans (6 December 2012). From Holomorphic Functions to Complex Manifolds. Springer. ISBN 9781468492736.
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Noguchi, Junjiro (2016). Analytic Function Theory of Several Variables Elements of Oka's Coherence (p.x). p. XVIII, 397. doi:10.1007/978-981-10-0291-5. ISBN 978-981-10-0289-2. S2CID 125752012.
Noguchi, Junjiro (2016). Analytic Function Theory of Several Variables Elements of Oka's Coherence (p.33). p. XVIII, 397. doi:10.1007/978-981-10-0291-5. ISBN 978-981-10-0289-2. S2CID 125752012.
Remmert, R. (1994). "Local Theory of Complex Spaces". Several Complex Variables VII §6. Calculs of Coherent sheaves. Encyclopaedia of Mathematical Sciences. Vol. 74. pp. 7–96. doi:10.1007/978-3-662-09873-8_2. ISBN 978-3-642-08150-7.
Ohsawa, Takeo (10 December 2018). L2 Approaches in Several Complex Variables: Towards the Oka–Cartan Theory with Precise Bounds. Springer Monographs in Mathematics. doi:10.1007/978-4-431-55747-0. ISBN 9784431568513.
Grauert, H.; Remmert, R. (6 December 2012). Coherent Analytic Sheaves. Springer. p. 60. ISBN 978-3-642-69582-7.
Grauert, H.; Remmert, R. (6 December 2012). Coherent Analytic Sheaves. Springer. p. 84. ISBN 978-3-642-69582-7.
Serre, Jean-Pierre (2003). "Quelques problèmes globaux rélatifs aux variétés de Stein". Oeuvres - Collected Papers I (in French). Springer Berlin Heidelberg. p. XXIII, 598. ISBN 978-3-642-39815-5.
Ohsawa, Takeo (10 December 2018). L2 Approaches in Several Complex Variables: Towards the Oka–Cartan Theory with Precise Bounds. Springer Monographs in Mathematics. doi:10.1007/978-4-431-55747-0. ISBN 9784431568513.
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Hartshorne, Robin (1977). Algebraic Geometry. Graduate Texts in Mathematics. Vol. 52. Berlin, New York: Springer-Verlag. doi:10.1007/978-1-4757-3849-0. ISBN 978-0-387-90244-9. MR 0463157. S2CID 197660097. Zbl 0367.14001.

college-de-france.fr

Serre, Jean-Pierre (1955), "Faisceaux algébriques cohérents" (PDF), Annals of Mathematics, 61 (2): 197–278, doi:10.2307/1969915, JSTOR 1969915, MR 0068874

doi.org

Hörmander, Lars (1965). "L² estimates and existence theorems for the ${\bar {\partial }}$ operator". Acta Mathematica. 113: 89–152. doi:10.1007/BF02391775. S2CID 120051843.
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Chen, So-Chin (2000). "Complex analysis in one and several variables". Taiwanese Journal of Mathematics. 4 (4): 531–568. doi:10.11650/twjm/1500407292. JSTOR 43833225. MR 1799753. Zbl 0974.32001.
Chong, C.T.; Leong, Y.K. (1986). "An interview with Jean-Pierre Serre". The Mathematical Intelligencer. 8 (4): 8–13. doi:10.1007/BF03026112. S2CID 121138963.
Freitag, Eberhard (2011). "Analytic Functions of Several Complex Variables". Complex Analysis 2. Universitext. pp. 300–346. doi:10.1007/978-3-642-20554-5_5. ISBN 978-3-642-20553-8.
Serre, Jean-Pierre (1956). "Géométrie algébrique et géométrie analytique". Annales de l'Institut Fourier (in French). 6: 1–42. doi:10.5802/aif.59. ISSN 0373-0956. MR 0082175. Zbl 0075.30401.
Ohsawa, Takeo (1984). "Vanishing theorems on complete Kähler manifolds". Publications of the Research Institute for Mathematical Sciences. 20: 21–38. doi:10.2977/prims/1195181825.
Field, M (1982). "Complex Manifolds". Several Complex Variables and Complex Manifolds I. pp. 134–186. doi:10.1017/CBO9781107325562.005. ISBN 9780521283014.
Poincare, M. Henri (1907). "Les fonctions analytiques de deux variables et la représentation conforme". Rendiconti del Circolo Matematico di Palermo. 23: 185–220. doi:10.1007/BF03013518. S2CID 123480258.
Siu, Yum-Tong (1991). "Uniformization in Several Complex Variables". In Wu, Hung-Hsi (ed.). Contemporary Geometry. p. 494. doi:10.1007/978-1-4684-7950-8. ISBN 978-1-4684-7950-8.
Jarnicki, Marek; Pflug, Peter (2008). First Steps in Several Complex Variables: Reinhardt Domains. doi:10.4171/049. ISBN 978-3-03719-049-4.
Sakai, Eiichi (1970). "Meromorphic or Holomorphic Completion of a Reinhardt Domain". Nagoya Mathematical Journal. 38: 1–12. doi:10.1017/S0027763000013465. S2CID 118248529.
Range, R. Michael (1986). "Domains of Holomorphy and Pseudoconvexity". Holomorphic Functions and Integral Representations in Several Complex Variables. Graduate Texts in Mathematics. Vol. 108. p. 10.1007/978-1-4757-1918-5_2. doi:10.1007/978-1-4757-1918-5_2. ISBN 978-1-4419-3078-1.
Krantz, Steven G. (2008). "The Hartogs extension phenomenon redux". Complex Variables and Elliptic Equations. 53 (4): 343–353. doi:10.1080/17476930701747716. S2CID 121700550.
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Merker, Joël; Porten, Egmont (2007). "A Morse-theoretical proof of the Hartogs extension theorem". Journal of Geometric Analysis. 17 (3): 513–546. arXiv:math/0610985. doi:10.1007/BF02922095. S2CID 449210.
Boggess, A.; Dwilewicz, R.J.; Slodkowski, Z. (2013). "Hartogs extension for generalized tubes in Cn". Journal of Mathematical Analysis and Applications. 402 (2): 574–578. doi:10.1016/j.jmaa.2013.01.049.
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Sunada, Toshikazu (1978). "Holomorphic equivalence problem for bounded Reinhardt domains". Mathematische Annalen. 235 (2): 111–128. doi:10.1007/BF01405009. S2CID 124324696.
Cartan, Henri; Thullen, Peter (1932). "Zur Theorie der Singularitäten der Funktionen mehrerer komplexen Veränderlichen Regularitäts-und Konvergenzbereiche". Mathematische Annalen. 106: 617–647. doi:10.1007/BF01455905.
Oka, Kiyoshi (1953), "Sur les fonctions analytiques de plusieurs variables. IX. Domaines finis sans point critique intérieur", Japanese Journal of Mathematics: Transactions and Abstracts, 23: 97–155, doi:10.4099/jjm1924.23.0_97, ISSN 0075-3432
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Oka, Kiyoshi (1950). "Sur les fonctions analytiques de plusieurs variables. VII. Sur quelques notions arithmétiques". Bulletin de la Société Mathématique de France. 2: 1–27. doi:10.24033/bsmf.1408., Oka, Kiyoshi (1961). "Sur les fonctions analytiques de plusieurs variables. VII. Sur quelques notions arithmétiques" (PDF). Iwanami Shoten, Tokyo (Oka's Original Version).^{[note 9]}
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Chorlay, Renaud (January 2010). "From Problems to Structures: the Cousin Problems and the Emergence of the Sheaf Concept". Archive for History of Exact Sciences. 64 (1): 1–73. doi:10.1007/s00407-009-0052-3. JSTOR 41342411. S2CID 73633995.
Sheaves on Manifolds. Grundlehren der mathematischen Wissenschaften. Vol. 136. 1990. doi:10.1007/978-3-662-02661-8. ISBN 978-3-642-08082-1.
Forstnerič, Franc (2011). "Stein Manifolds". Stein Manifolds and Holomorphic Mappings. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics. Vol. 56. doi:10.1007/978-3-642-22250-4. ISBN 978-3-642-22249-8.
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Oscar Zariski (1944), "Reduction of the Singularities of Algebraic Three Dimensional Varieties", Annals of Mathematics, Second Series, 45 (3): 472–542, doi:10.2307/1969189, JSTOR 1969189
Hans Grauert & Reinhold Remmert (1956), "Konvexität in der komplexen Analysis. Nicht-holomorph-konvexe Holomorphiegebiete und Anwendungen auf die Abbildungstheorie", Commentarii Mathematici Helvetici, 31: 152–183, doi:10.1007/BF02564357, S2CID 117913713, Zbl 0073.30301
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Noguchi, Junjiro (2019). "A brief chronicle of the Levi (Hartog's inverse) problem, coherence and open problem". Notices of the International Congress of Chinese Mathematicians. 7 (2): 19–24. arXiv:1807.08246. doi:10.4310/ICCM.2019.V7.N2.A2. S2CID 119619733.
Noguchi, Junjiro (2016). Analytic Function Theory of Several Variables Elements of Oka's Coherence (p.x). p. XVIII, 397. doi:10.1007/978-981-10-0291-5. ISBN 978-981-10-0289-2. S2CID 125752012.
Noguchi, Junjiro (2016). Analytic Function Theory of Several Variables Elements of Oka's Coherence (p.33). p. XVIII, 397. doi:10.1007/978-981-10-0291-5. ISBN 978-981-10-0289-2. S2CID 125752012.
Serre, Jean-Pierre (1955), "Faisceaux algébriques cohérents" (PDF), Annals of Mathematics, 61 (2): 197–278, doi:10.2307/1969915, JSTOR 1969915, MR 0068874
Grothendiec, Alexander; Dieudonn, Jean (1960). "Éléments de géométrie algébrique: I. Le langage des schémas (ch.0 § 5. FAISCEAUX QUASI-COHÉRENTS ET FAISCEAUX COHÉRENTS (0.5.1–0.5.3))". Publications Mathématiques de l'IHÉS. 4. doi:10.1007/bf02684778. MR 0217083. S2CID 121855488.
Remmert, R. (1994). "Local Theory of Complex Spaces". Several Complex Variables VII §6. Calculs of Coherent sheaves. Encyclopaedia of Mathematical Sciences. Vol. 74. pp. 7–96. doi:10.1007/978-3-662-09873-8_2. ISBN 978-3-642-08150-7.
Ohsawa, Takeo (10 December 2018). L2 Approaches in Several Complex Variables: Towards the Oka–Cartan Theory with Precise Bounds. Springer Monographs in Mathematics. doi:10.1007/978-4-431-55747-0. ISBN 9784431568513.
Noguchi, Junjiro (2019), "A Weak Coherence Theorem and Remarks to the Oka Theory" (PDF), Kodai Math. J., 42 (3): 566–586, arXiv:1704.07726, doi:10.2996/kmj/1572487232, S2CID 119697608
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