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
Recommended Citation
Ólafsson, G., & Pasquale, A. (2004). A Paley-Wiener theorem for the Θ-hypergeometric transform: The even multiplicity case. Journal des Mathematiques Pures et Appliquees, 83 (7), 869-927. https://doi.org/10.1016/j.matpur.2004.02.002
