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Potential theory associated with the Dunkl Laplacian

  • Kods Hassine EMAIL logo
Published/Copyright: May 19, 2017

Abstract

The main goal of this paper is to develop a potential theoretical approach to study the Dunkl Laplacian Δk, which is a standard example of differential-difference operators. Introducing the Green kernel relative to Δk, we prove that the Dunkl Laplacian generates a Balayage space and we investigate the associated family of harmonic measures. Therefore, by means of harmonic kernels, we give a characterization of all Δk-harmonic functions on a large class of open subsets U of d. We also establish existence and uniqueness results of a solution of the corresponding Dirichlet problem.

MSC 2010: 31B05; 31C40; 35J08

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Received: 2015-10-1
Revised: 2017-1-26
Accepted: 2017-4-1
Published Online: 2017-5-19
Published in Print: 2017-10-1

© 2017 Walter de Gruyter GmbH, Berlin/Boston

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