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

Bruno Schapira (1, 2)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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.

Mots clés: heat kernel; Differential-difference equations; hypergeometric functions; root systems; Schwartz space; heat kernel.

Domaines: Analyse classique [math.CA]

Bruno Schapira. Contributions to the hypergeometric function theory of Heckman and Opdam: sharp estimates, Schwartz space, heat kernel. 2006. ⟨hal-00023581⟩