Reproducing kernels for Dunkl polyharmonic polynomials

Commentationes mathematicae Universitatis Carolinae

Kamel Touahri¹ 

关键词: Dunkl Laplacian;    reproducing kernel;   

DOI  :  

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 摘 要 】

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.

【 授权许可】

CC BY