Kernel functions and conformal mapping

S. Bergman; M. Schiffer

Compositio Mathematica (1951)

  • Volume: 8, page 205-249
  • ISSN: 0010-437X

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Bergman, S., and Schiffer, M.. "Kernel functions and conformal mapping." Compositio Mathematica 8 (1951): 205-249. <http://eudml.org/doc/88763>.

@article{Bergman1951,
author = {Bergman, S., Schiffer, M.},
journal = {Compositio Mathematica},
keywords = {complex functions},
language = {eng},
pages = {205-249},
publisher = {Kraus Reprint},
title = {Kernel functions and conformal mapping},
url = {http://eudml.org/doc/88763},
volume = {8},
year = {1951},
}

TY - JOUR
AU - Bergman, S.
AU - Schiffer, M.
TI - Kernel functions and conformal mapping
JO - Compositio Mathematica
PY - 1951
PB - Kraus Reprint
VL - 8
SP - 205
EP - 249
LA - eng
KW - complex functions
UR - http://eudml.org/doc/88763
ER -

References

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  1. N. Aronszajn [1] La théorie des noyaux reproduisants et ses applications, I, Proc. Cam-bridge Phil. Soc., vol. 39 (1943), pp. 133—153. Zbl0061.26204
  2. S. Bergman [1] Sur les fonctions orthogonales de plusieurs variables complexes avec les applications a la théorie des fonctions analytiques, Interscience Publishers, New York, 1941, Memorial des Sciences Mathématiques, Fascicules 106 and 108, Paris1947—1948. Zbl0036.05101JFM67.0299.03
  3. [2] Partial differential equations, Advanced topics, Brown University, Providence1941. 
  4. S. Bergman M. Schiffer [1] A representation of Green's and Neumann's functions in the theory of partial differential equations of second order. Duke Math. J., vol. 14 (1947), pp. 609—638. Zbl0029.39901
  5. [2] On Green's and Neumann's functions in the theory of partial differential equations, Bull. Am. Math. Soc. vol. 53 (1947), pp. 1141-1151. Zbl0032.35201MR22974
  6. [3] Kernel functions in the theory of partial differential equations of elliptic type, Duke Math. J., vol. 15 (1948), pp. 535—566. Zbl0030.25503
  7. P.R. Garabedian [1] Schwarz' lemma and the Szegö kernel functions, Transactions Am. Math. Soc., vol. 67 (1949) pp. 1—35. Zbl0035.05402
  8. P.R. Garabedian— M. Schiffer [1] Identities in the theory of conformal mapping, Transactions Am. Math. Soc., vol. 65 (1949), pp. 187—238, Zbl0035.05204
  9. H. Grunsky [1] Koeffizientenbedingungen für schlicht abbildende meromorphe Funktionen, Math. Zeitschrift, vol. 45 (1939), pp. 29-61. Zbl0022.15103MR1545803JFM65.0339.04
  10. J. Hadamard [1] Leçons sur le calcul des variations, Paris, 1910. JFM41.0432.02
  11. P. LÉvy [1] Leçons d'Analyse fonctionelle, Paris, 1922. JFM48.0453.01
  12. Z. Nehari [1] The Schwarzian derivative and schlicht functions, Bull. Am. Math. Soc., vol. 55 (1949), pp. 545-551. Zbl0035.05104MR29999
  13. J. Plemelj [1] Ein Ergänzungssatz zur Cauchy'schen Integraldarstellung analytischer Funktionen, Randwerte betreffend, Monatsh. Math. Phys.19 (1908), pp. 205—210. Zbl39.0460.01JFM39.0460.01
  14. M. Schiffer [1] The span of multiply-connected domains, Duke Math. J., vol. 10 (1948), pp. 209—216. Zbl0060.23704
  15. [2] Hadamard's formula and variation of domain functions, Amer. J. Math., vol. 68 (1946), pp. 417—448. Zbl0060.23706
  16. [3] The kernel function of an orthonormal system, Duke Math. J., vol. 18 (1946), pp. 529-540. Zbl0060.23708MR19115
  17. [4] Faber polynomials in the theory of univalent functions, Bull. Am. Math. Soc., vol. 54 (1948). pp. 503—517. Zbl0033.36301
  18. [5] On different types of orthogonalization, Duke Math. J. vol. 17 (1950). 

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