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Transactions of the American Mathematical Society

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On inversion of the Bessel and Gelfand transforms

Authors: Masaaki Furusawa and Joseph A. Shalika
Journal: Trans. Amer. Math. Soc. 354 (2002), 837-852
MSC (2000): Primary 22E35; Secondary 11F70, 11F72
Published electronically: July 12, 2001
MathSciNet review: 1862570
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Abstract | References | Similar Articles | Additional Information


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.

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Additional Information

Masaaki Furusawa
Affiliation: Department of Mathematics, Graduate School of Science, Osaka City University, Sugimoto 3–3–138, Sumiyoshi-ku, Osaka 558–8585, Japan

Joseph A. Shalika
Affiliation: Department of Mathematics, The Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218

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. 10640028, the Ministry of Education, Science, Sports and Culture of Japan
Article copyright: © Copyright 2001 American Mathematical Society