Intertwining Operators Associated with Dihedral Groups

被引：0
作者：
Yuan Xu
机构：
[1] University of Oregon,Department of Mathematics
来源：
Constructive Approximation | 2020年 / 52卷
关键词：
Intertwining operator; Dunkl operators; Dihedral group; Orthogonal polynomials; Generating function; 33C45; 44A20; Secondary 33C50; 33C80;
D O I：
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学科分类号：
摘要：
The Dunkl operators associated with a dihedral group are a pair of differential-difference operators that generate a commutative algebra acting on differentiable functions in R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}^2$$\end{document}. The intertwining operator intertwines between this algebra and the algebra of differential operators. The main result of this paper is an integral representation of the intertwining operator on a class of functions. As an application, closed formulas for the Poisson kernels of h-harmonics and sieved Gegenbauer polynomials are deduced when one of the variables is at vertices of a regular polygon, and similar formulas are also derived for several other related families of orthogonal polynomials.
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页码：395 / 422
页数：27
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