Support properties of the intertwining and the mean value operators in Dunkl theory

Gallardo, Léonard; Rejeb, Chaabane

doi:10.1090/proc/13478

Support properties of the intertwining and the mean value operators in Dunkl theory
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by Léonard Gallardo and Chaabane Rejeb PDF

Proc. Amer. Math. Soc. 146 (2018), 145-152 Request permission

Abstract:

In this paper we show that the representing measures of the Dunkl intertwining operator associated to a Coxeter-Weyl group $W$ in $\mathbb {R}^d$ and to a multiplicity function $k\geq 0$, have $W$-invariant supports under the condition $k>0$. This property enables us to determine explicitly the supports of the measures representing the volume mean operator, a fundamental tool for the study of harmonic functions relative to the Dunkl-Laplacian operator.

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