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

Journal of the Mathematical Society of Japan

Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645

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

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2024 Volume 76 Issue 1 Pages 73-109

DOI https://doi.org/10.2969/jmsj/88728872

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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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