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Reproducing kernels for Dunkl polyharmonic polynomials

Kamel Touahri — 2012

Commentationes Mathematicae Universitatis Carolinae

In this paper, we compute explicitly the reproducing kernel of the space of homogeneous polynomials of degree n and Dunkl polyharmonic of degree m , i.e. Δ k m u = 0 , m { 0 } , where Δ k is the Dunkl Laplacian and we study the convergence of the orthogonal series of Dunkl polyharmonic homogeneous polynomials.

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