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Bounded harmonic functions for the Heckman--Opdam Laplacian

Bounded harmonic functions for the Heckman--Opdam Laplacian

Authors :
Bruno Schapira
Laboratoire de Mathématiques d'Orsay (LM-Orsay)
Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)
Publication Year :
2008
Publisher :
HAL CCSD, 2008.

Abstract

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.<br />Comment: [V2]: terminology "radial function" changed in "W-invariant function". One reference added

Details

Language :
English
Database :
OpenAIRE
Accession number :
edsair.doi.dedup.....49020bfb83c4b0c8af2d2afaf4902eaa