Inversion formula for the hypergeometric Fourier transform associated with a root system of type $BC$

Tatsuo HONDA; Hiroshi ODA; Nobukazu SHIMENO

doi:10.2969/jmsj/88728872

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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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

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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

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