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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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On inversion of the Bessel and Gelfand transforms
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by Masaaki Furusawa and Joseph A. Shalika
Trans. Amer. Math. Soc. 354 (2002), 837-852
DOI: https://doi.org/10.1090/S0002-9947-01-02866-5
Published electronically: July 12, 2001

Abstract:

We construct the Plancherel measure corresponding to the Bessel model on the split special orthogonal group of $\text {odd degree}\ge 5$ and the Whittaker model on a connected split reductive group in general. As an application we prove the inversion formula which expresses the related integral transform in terms of the Satake transform.
References
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Bibliographic Information
  • Masaaki Furusawa
  • Affiliation: Department of Mathematics, Graduate School of Science, Osaka City University, Sugimoto 3–3–138, Sumiyoshi-ku, OsakaΒ 558–8585, Japan
  • Email: furusawa@sci.osaka-cu.ac.jp
  • Joseph A. Shalika
  • Affiliation: Department of Mathematics, The Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218
  • Email: shalika@math.jhu.edu
  • Received by editor(s): August 7, 2000
  • Received by editor(s) in revised form: February 26, 2001
  • Published electronically: July 12, 2001
  • Additional Notes: The research of Furusawa was partially supported by the Sumitomo Foundation and the Grant-in-Aid for Scientific Research No.Β 10640028, the Ministry of Education, Science, Sports and Culture of Japan
  • © Copyright 2001 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 354 (2002), 837-852
  • MSC (2000): Primary 22E35; Secondary 11F70, 11F72
  • DOI: https://doi.org/10.1090/S0002-9947-01-02866-5
  • MathSciNet review: 1862570