Bounded harmonic functions for the Heckman--Opdam Laplacian

Bruno Schapira (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

We describe the set of bounded harmonic functions for the Heckman--Opdam Laplacian, when the multiplicity function is larger than $1/2$. We prove that this set is a vector space of dimension the cardinality of the Weyl group. We give some consequences in terms of the associated hypergeometric functions.

Mots clés: Trigonometric Dunkl theory; bounded harmonic function; Poisson boundary; mirror coupling

Domaines: Probabilités [math.PR]; Analyse classique [math.CA]

Bruno Schapira. Bounded harmonic functions for the Heckman--Opdam Laplacian. 2008. ⟨hal-00324368v2⟩