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• W1567678804 abstract "$G_lambda^{(alpha,beta)}(x)$ be the eigenfunctions of the Dunkl-Cherednik operator $T^{(alpha,beta)}$ on $mathbb{R}$, with $alphageq betageq -{1over 2}.$ 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 for the Dunkl kernels proved in cite{Ros}. We then define and study a convolution structure associated to $G_lambda^{(alpha,beta)}.$" @default.
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• W1567678804 date "2010-04-26" @default.
• W1567678804 modified "2023-09-27" @default.
• W1567678804 title "Opdam functions: product formula and convolution structure in dimension 1" @default.
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