A Paley-Wiener theorem for the $\Theta$-spherical transform: the even multiplicity case
Functional Analysis
2007-05-23 v1
Abstract
The -spherical functions generalize the spherical functions on Riemannian symmetric spaces and the spherical functions on non-compactly causal symmetric spaces. In this article we consider the case of even multiplicity functions. We construct a differential shift operator with smooth coefficients which generates the -spherical functions from finite sums of exponential functions. We then use this fact to prove a Paley-Wiener theorem for the -spherical transfrom.
Cite
@article{arxiv.math/0304361,
title = {A Paley-Wiener theorem for the $\Theta$-spherical transform: the even multiplicity case},
author = {Gestur Olafsson and Angela Pasquale},
journal= {arXiv preprint arXiv:math/0304361},
year = {2007}
}