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arXiv · 1608.03567

A Laplace-type representation of the generalized spherical functions associated to the root systems of type A

Patrice Sawyer
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Abstract

In this paper, we extend the iterative expression for the generalized spherical functions associated to the root systems of type $A$ previously obtained beyond regular elements. We also provide the corresponding expression in the flat case. From there, we derive a Laplace-type representation for the generalized spherical functions associated to the root systems of type $A$ in the Dunkl setting as well as in the trigonometric Dunkl setting. This representation leads us to describe precisely the support of the generalized Abel transform. Thanks to a recent result of Rejeb, this allows us to give the support for the Dunkl intertwining operator.

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Patrice Sawyer. 2016-08-11. A Laplace-type representation of the generalized spherical functions associated to the root systems of type A. https://arxiv.org/abs/1608.03567

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