English

A Paley-Wiener theorem for the $\Theta$-spherical transform: the even multiplicity case

Functional Analysis 2007-05-23 v1

Abstract

The Θ\Theta-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 DmD_m with smooth coefficients which generates the Θ\Theta-spherical functions from finite sums of exponential functions. We then use this fact to prove a Paley-Wiener theorem for the Θ\Theta-spherical transfrom.

Keywords

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}
}
R2 v1 2026-07-22T16:53:51.948Z