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AbstractThe main goal of this paper is to develop a potential theoretical approach to study the Dunkl Laplacian Δk{\Delta_{k}}, which is a standard example of differential-difference operators. Introducing the Green kernel relative to Δk{\Delta_{k}}, 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{\Delta_{k}}-harmonic functions on a large class of open subsets U of ℝd{\mathbb{R}^{d}}. We also establish existence and uniqueness results of a solution of the corresponding Dirichlet problem.
Advances in Pure and Applied Mathematics – de Gruyter
Published: Oct 1, 2017
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