2018/08/09 by Yuan Xu, Xu, Yuan
Mathematics · Physics and Astronomy · #33C45 #33C80 #44A20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical functions and polynomials #Nonlinear Waves and Solitons #Secondary 33C50
paper · pdf · doi:10.48550/arxiv.1808.03369
openalex publication_date 2018/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Dunkl operators associated to a dihedral group are a pair of differential-difference operators that generate a commutative algebra acting on differentiable functions in ℝ2. 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.