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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Characterization of the Hilbert ball by its automorphism group


Authors: Kang-Tae Kim and Steven G. Krantz
Journal: Trans. Amer. Math. Soc. 354 (2002), 2797-2818
MSC (2000): Primary 32A07
Published electronically: February 12, 2002
MathSciNet review: 1895204
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Abstract: Let $\Omega$ be a bounded, convex domain in a separable Hilbert space. The authors prove a version of the theorem of Bun Wong, which asserts that if such a domain admits an automorphism orbit accumulating at a strongly pseudoconvex boundary point, then it is biholomorphic to the ball. Key ingredients in the proof are a new localization argument using holomorphic peaking functions and the use of new ``normal families'' arguments in the construction of the limit biholomorphism.


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Additional Information

Kang-Tae Kim
Affiliation: Department of Mathematics, Pohang University of Science and Technology, Pohang 790-784, The Republic of Korea
Email: kimkt@postech.edu

Steven G. Krantz
Affiliation: Department of Mathematics, Washington University in St. Louis, St. Louis, Missouri 63130
Email: sk@math.wustl.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-02-02895-7
PII: S 0002-9947(02)02895-7
Received by editor(s): January 20, 2000
Received by editor(s) in revised form: March 23, 2001
Published electronically: February 12, 2002
Article copyright: © Copyright 2002 American Mathematical Society