Title

A Paley-Wiener theorem for the Θ-hypergeometric transform: The even multiplicity case

Document Type

Article

Publication Date

7-1-2004

Abstract

The Θ-hypergeometric functions generalize the spherical functions on Riemannian symmetric spaces and the spherical functions on non-compactly causal symmetric spaces. In this paper we consider the case of even multiplicity functions. We construct a differential shift operator Dm with smooth coefficients which generates the Θ-hypergeometric functions from finite sums of exponential functions. We then use this fact to prove a Paley-Wiener theorem for the Θ-hypergeometric transform. © 2004 Elsevier SAS. All rights reserved.

Publication Source (Journal or Book title)

Journal des Mathematiques Pures et Appliquees

First Page

869

Last Page

927

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