Title: Convolution and Elliptic Operators in Dunkl Theory
Abstract: We consider generalized convolutions in the rational Dunkl setting and give new results on the (singular) support of these convolutions. Furthermore, elliptic Dunkl operators are introduced, which are motivated by radial parts of elliptic operators on Riemannian symmetric spaces. The statements about the generalized convolution make it possible to prove a theorem on hypoellipticity for elliptic Dunkl operators, as well as a theorem on elliptic regularity on generalized Sobolev spaces. Depending on time, an outlook on the multitemporal wave equation in the Dunkl setting is given.
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