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

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

2006-05-02

arxiv.org/abs/math/0605045v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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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