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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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 “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
  • 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