Dunkl-Clifford分析框架下的Hermite多项式

Hermite Polynomials Related to the Dunkl-Clifford Analysis

本文从纯分析的角度出发,利用Dunkl-Dirac算子的球坐标表示,得到了Dunkl-Clifford分析框架下关于Dunkl算子任意正整数次幂,尤其是奇数次幂下经典Hermite多项式的推广形式。并且作为应用,本文建立了Dunkl-Clifford分析中Hermite多项式所满足的微分方程。

In this paper,based on the classical method from Clifford analysis and a spherical representation of Dunkl-Dirac operator,ageneralization of the classical Hermite polynomials related to the framework of Dunkl operators is presented.For application,the associated differential equation about Hermite polynomials in Dunkl-Clifford analysis setting is established.