Characterization of the Hilbert ball by its automorphism group
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- by Kang-Tae Kim and Steven G. Krantz PDF
- Trans. Amer. Math. Soc. 354 (2002), 2797-2818 Request permission
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 ânormal familiesâ arguments in the construction of the limit biholomorphism.References
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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
- MR Author ID: 106160
- Email: sk@math.wustl.edu
- Received by editor(s): January 20, 2000
- Received by editor(s) in revised form: March 23, 2001
- Published electronically: February 12, 2002
- © Copyright 2002 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 354 (2002), 2797-2818
- MSC (2000): Primary 32A07
- DOI: https://doi.org/10.1090/S0002-9947-02-02895-7
- MathSciNet review: 1895204