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Proceedings of the American Mathematical Society

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Holomorphic mappings between balls and polydiscs

Author: R. R. Simha
Journal: Proc. Amer. Math. Soc. 54 (1976), 241-242
MSC: Primary 32A07
MathSciNet review: 0402100
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Abstract: A proof based only on Schwarz's lemma is given for the fact that the polydisc and the ball are not holomorphically equivalent.

References [Enhancements On Off] (What's this?)

  • [1] H. Alexander, Holomorphic mappings from the ball and polydisc, Math. Ann. 209 (1974), 249–256. MR 0352531
  • [2] C. Carathéodory, Über die Abbildungen, die durch Systeme von analytischen Funktionen von mehreren Veränderlichen erzeugt werden, Math. Z. 34 (1932), no. 1, 758–792 (German). MR 1545283, 10.1007/BF01180619
  • [3] F. Riesz and B. Sz.-Nagy, Leçons d'analyse fonctionnelle, 4th ed., Gauthier-Villars, Paris, 1965; English transl. of 2nd ed., Ungar, 1955. MR 17, 175; 31 #3815.

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Article copyright: © Copyright 1976 American Mathematical Society