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Pizzetti Series and Polyharmonicity Associated with the Dunkl Laplacian

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Abstract

In this paper we are concerned with the Pizzetti series associated with the Dunkl Laplacian denoted Δ k . We study the convergence of this series and we give some applications. Next we establish some properties of polyharmonic functions associated with Δ k , especially, we establish Liouville type results.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences of Tunis, Campus Universitaire, 2092, Tunis, Tunisia

    Nejib Ben Salem & Kamel Touahri

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  1. Nejib Ben Salem
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  2. Kamel Touahri
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Correspondence to Nejib Ben Salem.

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Salem, N.B., Touahri, K. Pizzetti Series and Polyharmonicity Associated with the Dunkl Laplacian. Mediterr. J. Math. 7, 455–470 (2010). https://doi.org/10.1007/s00009-010-0055-y

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  • DOI: https://doi.org/10.1007/s00009-010-0055-y

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