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On a Theorem of Bers, with Applications to the Study of Automorphism Groups of Domains

  Published:2016-02-03
 Printed: Jun 2016
  • Steven Krantz,
    Department of Mathematics, Washington University in St. Louis, St. Louis, Missouri 63130
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Abstract

We study and generalize a classical theorem of L. Bers that classifies domains up to biholomorphic equivalence in terms of the algebras of holomorphic functions on those domains. Then we develop applications of these results to the study of domains with noncompact automorphism group.
Keywords: Bers's theorem, algebras of holomorphic functions, noncompact automorphism group, biholomorphic equivalence Bers's theorem, algebras of holomorphic functions, noncompact automorphism group, biholomorphic equivalence
MSC Classifications: 32A38, 30H50, 32A10, 32M99 show english descriptions Algebras of holomorphic functions [See also 30H05, 46J10, 46J15]
Algebras of analytic functions
Holomorphic functions
None of the above, but in this section
32A38 - Algebras of holomorphic functions [See also 30H05, 46J10, 46J15]
30H50 - Algebras of analytic functions
32A10 - Holomorphic functions
32M99 - None of the above, but in this section
 

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