Geodesic
Reproducing kernels for Dunkl polyharmonic polynomials
Commentationes Mathematicae Universitatis Carolinae, Tome 53 (2012) no. 1, pp. 37-50.

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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. $\Delta_{k}^{m}u=0$, $m\in \mathbb{N}\setminus\{0\}$, where $\Delta_{k}$ is the Dunkl Laplacian and we study the convergence of the orthogonal series of Dunkl polyharmonic homogeneous polynomials.
Classification : 31B30, 33C55
Keywords: Dunkl Laplacian; reproducing kernel 
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     title = {Reproducing kernels for {Dunkl} polyharmonic polynomials},
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Touahri, Kamel. Reproducing kernels for Dunkl polyharmonic polynomials. Commentationes Mathematicae Universitatis Carolinae, Tome 53 (2012) no. 1, pp. 37-50. http://geodesic.mathdoc.fr/item/CMUC_2012__53_1_a2/