2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171857We 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.[V2]: terminology "radial function" changed in "W-invariant function". One reference addedProbabilityClassical Analysis and ODEs33C67; 60J45; 60J50text