Amédée Debiard

Espaces Hp au dessus de l'espace hermitien hyperbolique de Cn (n > 1), II

Abstract Growth of harmonic functions and boundary values in a Sobolev space; comparison between the H p space associated to Calderon Lusins area integral and the H p space associated to the maximal admissible function; study of Littlewood-Paley functions for the harmonic functions for the invariant laplacian of the hermitian hyperbolic space; relation between a Littlewood-Paley function and the bounded mean oscillation functions; study of H 1 and H 1 B.M.O. duality.

Représentation intégrale de certaines séries de fonctions sphériques d'un système de racines BC

Abstract We give an integral representation of the series of generalized Jacobi polynomials P ( n 0···0) ( αβγ ) which are in the kernel of the invariant operators of order greater than two on a root system BC p .

Hypergeometric symbolic calculus. I – Systems of two symbolic hypergeometric equations

Abstract We define a new hypergeometric symbolic calculus which allows the determination of the general solutions of two variables hypergeometric partial differential equations. We apply this method to the determination of a basis of the vector space of solutions of the 14 systems of Appell–Kampe de Feriet and Horn, as well as new integral representations for the solutions.

The universal Lie algebra associatedto a root system I

To any classical root system, one can associate a universal infinite dimensional Lie algebra of second order differential operators. In this work, we study this Lie algebra for rank 3 root system and show that it is semi simple, we show that it is related to the Eulerian polynomials.