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arXiv · 1511.06638

Potential theory associated with the Dunkl Laplacian

Kods Hassine
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Abstract

The main goal of this paper is to give potential theoretical approach to study the Dunkl Laplacian $Δ_k$ which is a standard example of differential-difference operators. By introducing the Green kernel relative to $Δ_k$, we prove that the Dunkl Laplacian generates a balayage space and we investigate the associated family of harmonic measures. Therefore, by mean of harmonic kernels, we give a characterization of all $Δ_k$-harmonic functions on large class of open subsets $U$ of $\mathbb{R}^d$. We also establish existence and uniqueness result of a solution of the corresponding Dirichlet problem.

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Kods Hassine. 2015-11-12. Potential theory associated with the Dunkl Laplacian. https://arxiv.org/abs/1511.06638

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