An application of hypergeometric shift operators to the chi-spherical Fourier transform

@article{Ho2015AnAO,
title={An application of hypergeometric shift operators to the chi-spherical Fourier transform},
author={Vivian M. Ho and Gestur {\'O}lafsson},
journal={arXiv: Classical Analysis and ODEs},
year={2015}
}
• Published 1 December 2015
• Mathematics
• arXiv: Classical Analysis and ODEs
We study the action of hypergeometric shift operators on the Heckman-Opdam hypergeometric functions associated with the $BC_n$ type root system and some negative multiplicities. Those hypergeometric functions are connected to the $\chi$-spherical functions on Hermitian symmetric spaces $U/K$ where $\chi$ 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… Expand
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