Laplace-type representation for some generalized spherical functions of type BC
Abstract
In [M. R\"osler and M. Voit. Integral Representation and Uniform Limits for Some Heckman-Opdam Hypergeometric Functions of type BC, Transactions of the American Mathematical Society, Vol. 368, No. 8, 6005-6032, 2016.], R\"osler and Voit give a formula for generalized spherical functions of type in terms of the spherical functions of type A. We use this formula to describe precisely the support of the associated generalized Abel transform. Furthermore, we derive a similar formula for the generalized spherical functions in the rational Dunkl setting. The support of the intertwining operator V is also deduced. We also show, as a consequence, that a Laplace-type expression exists for the generalized spherical functions both in the trigonometric Dunkl setting and in the rational Dunkl setting.
Cite
@article{arxiv.1707.04163,
title = {Laplace-type representation for some generalized spherical functions of type BC},
author = {P. Sawyer},
journal= {arXiv preprint arXiv:1707.04163},
year = {2017}
}