狄拉克δ函数 (Chinese Wikipedia)

Analysis of information sources in references of the Wikipedia article "狄拉克δ函数" in Chinese language version.

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ams.org

詳盡歷史請見：van der Pol & Bremmer 1987，§V.4。 van der Pol, Balth.; Bremmer, H., Operational calculus 3rd, New York: Chelsea Publishing Co., 1987, ISBN 978-0-8284-0327-6, MR 0904873
用Lang (1997)的方法表達，費耶核是一種狄拉克序列，而狄利克雷核則不是。 Lang, Serge, Undergraduate analysis, Undergraduate Texts in Mathematics 2nd, Berlin, New York: Springer-Verlag, 1997, ISBN 978-0-387-94841-6, MR 1476913
Bartle 1995，第xii+179頁. Bartle, Robert G. The elements of integration and Lebesgue measure. Wiley Classics Library. New York: John Wiley & Sons Inc. 1995. xii+179. ISBN 0-471-04222-6. MR 1312157.
Hörmander 1983，Theorem 2.1.5. Hörmander, L., The analysis of linear partial differential operators I, Grundl. Math. Wissenschaft. 256, Springer, 1983, ISBN 3-540-12104-8, MR 0717035
Hörmander 1983，§3.1. Hörmander, L., The analysis of linear partial differential operators I, Grundl. Math. Wissenschaft. 256, Springer, 1983, ISBN 3-540-12104-8, MR 0717035
Hörmander 1983，§8.2. Hörmander, L., The analysis of linear partial differential operators I, Grundl. Math. Wissenschaft. 256, Springer, 1983, ISBN 3-540-12104-8, MR 0717035
Dieudonné 1972，§17.3.3. Dieudonné, Jean, Treatise on analysis. Vol. III, Boston, Massachusetts: Academic Press, 1972, MR 0350769
Federer 1969，§2.5.19. Federer, Herbert, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften 153, New York: Springer-Verlag: xiv+676, 1969, ISBN 978-3-540-60656-7, MR 0257325
Hörmander 1983，§6.1. Hörmander, L., The analysis of linear partial differential operators I, Grundl. Math. Wissenschaft. 256, Springer, 1983, ISBN 3-540-12104-8, MR 0717035
Hörmander 1983，第56頁. Hörmander, L., The analysis of linear partial differential operators I, Grundl. Math. Wissenschaft. 256, Springer, 1983, ISBN 3-540-12104-8, MR 0717035
Hörmander 1983，§7.8. Hörmander, L., The analysis of linear partial differential operators I, Grundl. Math. Wissenschaft. 256, Springer, 1983, ISBN 3-540-12104-8, MR 0717035
Lang 1997，第312頁. Lang, Serge, Undergraduate analysis, Undergraduate Texts in Mathematics 2nd, Berlin, New York: Springer-Verlag, 1997, ISBN 978-0-387-94841-6, MR 1476913
Hörmander 1983，§7.2. Hörmander, L., The analysis of linear partial differential operators I, Grundl. Math. Wissenschaft. 256, Springer, 1983, ISBN 3-540-12104-8, MR 0717035

arxiv.org

Lange 2012，pp.29–30. Lange, Rutger-Jan, Potential theory, path integrals and the Laplacian of the indicator, Journal of High Energy Physics (Springer), 2012, 2012 (11): 29–30 [2014-10-30], Bibcode:2012JHEP...11..032L, arXiv:1302.0864 , doi:10.1007/JHEP11(2012)032, （原始内容存档于2021-04-19）
de la Madrid, Bohm & Gadella 2002. de la Madrid, R.; Bohm, A.; Gadella, M., Rigged Hilbert Space Treatment of Continuous Spectrum, Fortschr. Phys., 2002, 50 (2): 185–216, Bibcode:2002ForPh..50..185D, arXiv:quant-ph/0109154 , doi:10.1002/1521-3978(200203)50:2<185::AID-PROP185>3.0.CO;2-S

bnf.fr

gallica.bnf.fr

參見：Des intégrales doubles qui se présentent sous une forme indéterminèe

books.google.com

要以狄拉克符號來表達這一節的內容，可見Levin 2002，Coordinate-space wave functions and completeness, pp.=109ff Levin, Frank S., Coordinate-space wave functions and completeness, An introduction to quantum theory, Cambridge University Press: 109ff, 2002, ISBN 0-521-59841-9
Fourier 1822，第408頁. Fourier, J.B. The Analytical Theory of Heat English translation by Alexander Freeman, 1878. The University Press. 1822: 408 [2016-12-08]. （原始内容存档于2021-04-19）. , cf p 449 and pp 546–551. 法文原始文本请参见这里（页面存档备份，存于互联网档案馆）
Komatsu 2002，第200頁. Komatsu, Hikosaburo. Fourier's hyperfunctions and Heaviside's pseudodifferential operators. Takahiro Kawai; Keiko Fujita (编). Microlocal Analysis and Complex Fourier Analysis. World Scientific. 2002: 200 [2016-12-08]. ISBN 981-238-161-9. （原始内容存档于2021-04-19）.
Myint-U. & Debnath 2007，第4頁. Myint-U., Tyn; Debnath, Lokenath. Linear Partial Differential Equations for Scientists And Engineers 4th. Springer. 2007: 4 [2016-12-08]. ISBN 0-8176-4393-1. （原始内容存档于2021-04-02）.
Debnath & Bhatta 2007，第2頁. Debnath, Lokenath; Bhatta, Dambaru. Integral Transforms And Their Applications 2nd. CRC Press. 2007: 2 [2016-12-08]. ISBN 1-58488-575-0. （原始内容存档于2021-04-19）.
Grattan-Guinness 2009，第653頁. Grattan-Guinness, Ivor. Convolutions in French Mathematics, 1800–1840: From the Calculus and Mechanics to Mathematical Analysis and Mathematical Physics, Volume 2. Birkhäuser. 2009: 653 [2016-12-08]. ISBN 3-7643-2238-1. （原始内容存档于2021-04-19）.
Mitrović & Žubrinić 1998，第62頁. Mitrović, Dragiša; Žubrinić, Darko. Fundamentals of Applied Functional Analysis: Distributions, Sobolev Spaces. CRC Press. 1998: 62 [2016-12-08]. ISBN 0-582-24694-6. （原始内容存档于2021-04-19）.
Kracht & Kreyszig 1989，第553頁. Kracht, Manfred; Kreyszig, Erwin. On singular integral operators and generalizations. Themistocles M. Rassias (编). Topics in Mathematical Analysis: A Volume Dedicated to the Memory of A.L. Cauchy. World Scientific. 1989: 553 [2016-12-08]. ISBN 9971-5-0666-1. （原始内容存档于2021-04-19）.
Saichev & Woyczyński 1997，§1.1 The "delta function" as viewed by a physicist and an engineer, p. 3. Saichev, A I; Woyczyński, Wojbor Andrzej, Chapter1: Basic definitions and operations, Distributions in the Physical and Engineering Sciences: Distributional and fractal calculus, integral transforms, and wavelets, Birkhäuser, 1997, ISBN 0-8176-3924-1
Davis & Thomson 2000，Perfect operators, p.344. Davis, Howard Ted; Thomson, Kendall T, Linear algebra and linear operators in engineering with applications in Mathematica, Academic Press, 2000, ISBN 0-12-206349-X
Davis & Thomson 2000，Equation 8.9.11, p. 344. Davis, Howard Ted; Thomson, Kendall T, Linear algebra and linear operators in engineering with applications in Mathematica, Academic Press, 2000, ISBN 0-12-206349-X
Hartmann 1997，第154–155頁. Hartmann, William M., Signals, sound, and sensation, Springer, 1997 [2016-12-06], ISBN 978-1-56396-283-7, （原始内容存档于2021-04-19）

doi.org

dx.doi.org

參見：Laugwitz 1989 Laugwitz, D., Definite values of infinite sums: aspects of the foundations of infinitesimal analysis around 1820, Arch. Hist. Exact Sci., 1989, 39 (3): 195–245, doi:10.1007/BF00329867
Laugwitz 1989，第230頁. Laugwitz, D., Definite values of infinite sums: aspects of the foundations of infinitesimal analysis around 1820, Arch. Hist. Exact Sci., 1989, 39 (3): 195–245, doi:10.1007/BF00329867
Lange 2012，pp.29–30. Lange, Rutger-Jan, Potential theory, path integrals and the Laplacian of the indicator, Journal of High Energy Physics (Springer), 2012, 2012 (11): 29–30 [2014-10-30], Bibcode:2012JHEP...11..032L, arXiv:1302.0864 , doi:10.1007/JHEP11(2012)032, （原始内容存档于2021-04-19）
de la Madrid, Bohm & Gadella 2002. de la Madrid, R.; Bohm, A.; Gadella, M., Rigged Hilbert Space Treatment of Continuous Spectrum, Fortschr. Phys., 2002, 50 (2): 185–216, Bibcode:2002ForPh..50..185D, arXiv:quant-ph/0109154 , doi:10.1002/1521-3978(200203)50:2<185::AID-PROP185>3.0.CO;2-S

google.co.uk

books.google.co.uk

Dennis & Warren 2009，第230頁，chapter 4.5. Dennis, G. Zill; Warren, S. Wright. 4.5. Advanced Engineering Mathematics. 2009: 230 [2016-12-08]. ISBN 9780763782412. （原始内容存档于2021-04-19）.

harvard.edu

ui.adsabs.harvard.edu

Lange 2012，pp.29–30. Lange, Rutger-Jan, Potential theory, path integrals and the Laplacian of the indicator, Journal of High Energy Physics (Springer), 2012, 2012 (11): 29–30 [2014-10-30], Bibcode:2012JHEP...11..032L, arXiv:1302.0864 , doi:10.1007/JHEP11(2012)032, （原始内容存档于2021-04-19）
de la Madrid, Bohm & Gadella 2002. de la Madrid, R.; Bohm, A.; Gadella, M., Rigged Hilbert Space Treatment of Continuous Spectrum, Fortschr. Phys., 2002, 50 (2): 185–216, Bibcode:2002ForPh..50..185D, arXiv:quant-ph/0109154 , doi:10.1002/1521-3978(200203)50:2<185::AID-PROP185>3.0.CO;2-S

springer.com

link.springer.com

Lange 2012，pp.29–30. Lange, Rutger-Jan, Potential theory, path integrals and the Laplacian of the indicator, Journal of High Energy Physics (Springer), 2012, 2012 (11): 29–30 [2014-10-30], Bibcode:2012JHEP...11..032L, arXiv:1302.0864 , doi:10.1007/JHEP11(2012)032, （原始内容存档于2021-04-19）

web.archive.org

Dennis & Warren 2009，第230頁，chapter 4.5. Dennis, G. Zill; Warren, S. Wright. 4.5. Advanced Engineering Mathematics. 2009: 230 [2016-12-08]. ISBN 9780763782412. （原始内容存档于2021-04-19）.
Fourier 1822，第408頁. Fourier, J.B. The Analytical Theory of Heat English translation by Alexander Freeman, 1878. The University Press. 1822: 408 [2016-12-08]. （原始内容存档于2021-04-19）. , cf p 449 and pp 546–551. 法文原始文本请参见这里（页面存档备份，存于互联网档案馆）
Komatsu 2002，第200頁. Komatsu, Hikosaburo. Fourier's hyperfunctions and Heaviside's pseudodifferential operators. Takahiro Kawai; Keiko Fujita (编). Microlocal Analysis and Complex Fourier Analysis. World Scientific. 2002: 200 [2016-12-08]. ISBN 981-238-161-9. （原始内容存档于2021-04-19）.
Myint-U. & Debnath 2007，第4頁. Myint-U., Tyn; Debnath, Lokenath. Linear Partial Differential Equations for Scientists And Engineers 4th. Springer. 2007: 4 [2016-12-08]. ISBN 0-8176-4393-1. （原始内容存档于2021-04-02）.
Debnath & Bhatta 2007，第2頁. Debnath, Lokenath; Bhatta, Dambaru. Integral Transforms And Their Applications 2nd. CRC Press. 2007: 2 [2016-12-08]. ISBN 1-58488-575-0. （原始内容存档于2021-04-19）.
Grattan-Guinness 2009，第653頁. Grattan-Guinness, Ivor. Convolutions in French Mathematics, 1800–1840: From the Calculus and Mechanics to Mathematical Analysis and Mathematical Physics, Volume 2. Birkhäuser. 2009: 653 [2016-12-08]. ISBN 3-7643-2238-1. （原始内容存档于2021-04-19）.
Mitrović & Žubrinić 1998，第62頁. Mitrović, Dragiša; Žubrinić, Darko. Fundamentals of Applied Functional Analysis: Distributions, Sobolev Spaces. CRC Press. 1998: 62 [2016-12-08]. ISBN 0-582-24694-6. （原始内容存档于2021-04-19）.
Kracht & Kreyszig 1989，第553頁. Kracht, Manfred; Kreyszig, Erwin. On singular integral operators and generalizations. Themistocles M. Rassias (编). Topics in Mathematical Analysis: A Volume Dedicated to the Memory of A.L. Cauchy. World Scientific. 1989: 553 [2016-12-08]. ISBN 9971-5-0666-1. （原始内容存档于2021-04-19）.
Lange 2012，pp.29–30. Lange, Rutger-Jan, Potential theory, path integrals and the Laplacian of the indicator, Journal of High Energy Physics (Springer), 2012, 2012 (11): 29–30 [2014-10-30], Bibcode:2012JHEP...11..032L, arXiv:1302.0864 , doi:10.1007/JHEP11(2012)032, （原始内容存档于2021-04-19）
Hartmann 1997，第154–155頁. Hartmann, William M., Signals, sound, and sensation, Springer, 1997 [2016-12-06], ISBN 978-1-56396-283-7, （原始内容存档于2021-04-19）