Dunkl convolution and elliptic regularity for Dunkl operators
Classical Analysis and ODEs
2023-08-16 v1
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.
Keywords
Cite
@article{arxiv.2308.07710,
title = {Dunkl convolution and elliptic regularity for Dunkl operators},
author = {Dominik Brennecken},
journal= {arXiv preprint arXiv:2308.07710},
year = {2023}
}