Contributions to the hypergeometric function theory of Heckman and Opdam: sharp estimates, Schwartz space, heat kernel
Abstract
Under the assumption of positive multiplicity, we obtain basic estimates of the hypergeometric functions F\ and G\ 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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