Reproducing kernels for Dunkl polyharmonic polynomials

Kamel Touahri

Commentationes Mathematicae Universitatis Carolinae (2012)

  • Volume: 53, Issue: 1, page 37-50
  • ISSN: 0010-2628

Abstract

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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. Δ k m u = 0 , m ∈ ℕ ∖ { 0 } , where Δ k is the Dunkl Laplacian and we study the convergence of the orthogonal series of Dunkl polyharmonic homogeneous polynomials.

How to cite

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Touahri, Kamel. "Reproducing kernels for Dunkl polyharmonic polynomials." Commentationes Mathematicae Universitatis Carolinae 53.1 (2012): 37-50. <http://eudml.org/doc/246209>.

@article{Touahri2012,
abstract = {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 \lbrace 0\rbrace $, where $\Delta _\{k\}$ is the Dunkl Laplacian and we study the convergence of the orthogonal series of Dunkl polyharmonic homogeneous polynomials.},
author = {Touahri, Kamel},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Dunkl Laplacian; reproducing kernel; Dunkl Laplacian; reproducing kernel},
language = {eng},
number = {1},
pages = {37-50},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Reproducing kernels for Dunkl polyharmonic polynomials},
url = {http://eudml.org/doc/246209},
volume = {53},
year = {2012},
}

TY - JOUR
AU - Touahri, Kamel
TI - Reproducing kernels for Dunkl polyharmonic polynomials
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2012
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 53
IS - 1
SP - 37
EP - 50
AB - 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 \lbrace 0\rbrace $, where $\Delta _{k}$ is the Dunkl Laplacian and we study the convergence of the orthogonal series of Dunkl polyharmonic homogeneous polynomials.
LA - eng
KW - Dunkl Laplacian; reproducing kernel; Dunkl Laplacian; reproducing kernel
UR - http://eudml.org/doc/246209
ER -

References

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  2. Dunkl C.F., Xu Y., Orthogonal Polynomials of Several Variables, Cambridge Univ. Press, Cambridge, 2001. Zbl0964.33001MR1827871
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  7. Rösler M., 10.1007/3-540-44945-0_3, (Leuven, 2002), Lecture Notes in Mathematics, 1817, Springer, Berlin, 2003, pp. 93–135. MR2022853DOI10.1007/3-540-44945-0_3
  8. Rösler M., 10.1007/s002200050307, Comm. Math. Phys. 192 (1998), 519–542. MR1620515DOI10.1007/s002200050307
  9. Trimèche K., 10.1080/10652460108819358, Integral Transform. Spec. Funct. 12 (2001), no. 4, 349–374. MR1872375DOI10.1080/10652460108819358

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