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arXiv · 2308.07710

Dunkl convolution and elliptic regularity for Dunkl operators

Dominik Brennecken
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Abstract

We discuss in which cases the Dunkl convolution of distributions, possibly both with non-compact support, can be defined and study its analytic properties. We prove results on the (singular-)support of Dunkl convolutions. Based on this, we are able to prove a theorem on elliptic regularity for a certain class of Dunkl operators, called elliptic Dunkl operators. Finally, for the root systems of type A we consider the Dunkl-type Riesz distributions, prove that their Dunkl convolution exists and compute their convolution.

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Dominik Brennecken. 2023-08-15. Dunkl convolution and elliptic regularity for Dunkl operators. https://arxiv.org/abs/2308.07710

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