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Dunkl convolution and elliptic regularity for Dunkl operators
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AbstractWe 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 system we consider the Riesz distributions and prove that their Dunkl convolution exists and that holds.
Title: Dunkl convolution and elliptic regularity for Dunkl operators
Description:
AbstractWe 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 system we consider the Riesz distributions and prove that their Dunkl convolution exists and that holds.
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