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}
}
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
Inversion formula for the hypergeometric Fourier transform associated with a root system of type $BC$
We give the inversion formula and the Plancherel formula for the hypergeometric Fourier transform associated with a root system of type $BC$, when the multiplicity parameters are not necessarilyExpand

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