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.
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.
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/
@article{CMUC_2012_53_1_a2,
author = {Touahri, Kamel},
title = {Reproducing kernels for {Dunkl} polyharmonic polynomials},
journal = {Commentationes Mathematicae Universitatis Carolinae},
pages = {37--50},
year = {2012},
volume = {53},
number = {1},
mrnumber = {2880909},
zbl = {1249.33011},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMUC_2012_53_1_a2/}
}