January, 2024 Inversion formula for the hypergeometric Fourier transform associated with a root system of type $BC$
Tatsuo HONDA, Hiroshi ODA, Nobukazu SHIMENO
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J. Math. Soc. Japan 76(1): 73-109 (January, 2024). DOI: 10.2969/jmsj/88728872

Abstract

We give the inversion formula and the Plancherel formula for the hypergeometric Fourier transform associated with a root system of type $BC$, when the multiplicity parameters are not necessarily non-negative.

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Tatsuo HONDA. Hiroshi ODA. Nobukazu SHIMENO. "Inversion formula for the hypergeometric Fourier transform associated with a root system of type $BC$." J. Math. Soc. Japan 76 (1) 73 - 109, January, 2024. https://doi.org/10.2969/jmsj/88728872

Information

Received: 5 January 2022; Revised: 5 June 2022; Published: January, 2024
First available in Project Euclid: 5 December 2022

Digital Object Identifier: 10.2969/jmsj/88728872

Subjects:
Primary: 33C67
Secondary: 43A90

Keywords: Heckman–Opdam hypergeometric function , hypergeometric Fourier transform , Jacobi function , spherical function

Rights: Copyright ©2024 Mathematical Society of Japan

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Vol.76 • No. 1 • January, 2024
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