An application of hypergeometric shift operators to the χ-spherical fourier transform

Document Type

Article

Publication Date

1-1-2015

Abstract

We study the action of hypergeometric shift operators on the Heckman-Opdam hypergeometric functions associated with the BCn type root system and some negative multiplicities. Those hypergeometric functions are connected to the χ-spherical functions on Hermitian symmetric spaces U/K where χ is a nontrivial character of K. We apply shift operators to the hypergeometric functions to move negative multiplicities to positive ones. This allows us to use many well-known results of the hypergeometric functions associated with positive multiplicities. In particular, we use this technique to achieve exponential estimates for the χ-spherical functions. The motive comes from the Paley-Wiener type theorem on line bundles over Hermitian symmetric spaces.

Publication Source (Journal or Book title)

Contemporary Mathematics

First Page

143

Last Page

155

This document is currently not available here.

Share

COinS