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Contributions to the hypergeometric function theory of Heckman and Opdam: sharp estimates, Schwartz space, heat kernel

Bruno Schapira
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Abstract

Under the assumption of positive multiplicity, we obtain basic estimates of the hypergeometric functions F\_\la and G\_\la of Heckman and Opdam, and sharp estimates of the particular functions F\_0 and G\_0. Next we prove the Paley-Wiener theorem for the Schwartz class, solve the heat equation and estimate the heat kernel.

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Bruno Schapira. 2006-05-02. Contributions to the hypergeometric function theory of Heckman and Opdam: sharp estimates, Schwartz space, heat kernel. https://arxiv.org/abs/math/0605045

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