Opdam's hypergeometric functions: product formula and convolution structure in dimension 1

Autor:	Anker, Jean-Philippe, Ayadi, Fatma, Sifi, Mohamed
Rok vydání:	2010
Předmět:	Mathematics - Classical Analysis and ODEs Mathematics - Functional Analysis
Druh dokumentu:	Working Paper
Popis:	Let $G_{\lambda}^{(\alpha,\beta)}$ be the eigenfunctions of the Dunkl-Cherednik operator $T^{(\alpha,\beta)}$ on $\mathbb{R}$. In this paper we express the product $G_{\lambda}^{(\alpha,\beta)}(x)G_{\lambda}^{(\alpha,\beta)}(y)$ as an integral in terms of $G_{\lambda}^{(\alpha,\beta)}(z)$ with an explicit kernel. In general this kernel is not positive. Furthermore, by taking the so-called rational limit, we recover the product formula of M. R\"osler for the Dunkl kernel. We then define and study a convolution structure associated to $G_{\lambda}^{(\alpha,\beta)}$. Comment: Adv. Pure Appl. Math. (2011) 27 pp
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1004.5203 Zobrazit plný text záznamu View this record from Arxiv