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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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 (50 #5018)
  • [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, http://dx.doi.org/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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0402100-5
PII: S 0002-9939(1976)0402100-5
Article copyright: © Copyright 1976 American Mathematical Society