Advances in Pure and Applied Mathematics
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Opdam's hypergeometric functions: product formula and convolution structure in dimension 1
Let be the eigenfunctions of the Dunkl–Cherednik operator on . In this paper we express the product as an integral in terms of 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. Rösler for the Dunkl kernel. We then define and study a convolution structure associated to .
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