Bounded harmonic functions for the Heckman--Opdam Laplacian

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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.
[V2]: terminology "radial function" changed in "W-invariant function". One reference added

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Probability, Classical Analysis and ODEs, 33C67; 60J45; 60J50

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http://salesiana.dossiersoluciones.com/handle/123456789/171857

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0809.4232
 http://arxiv.org/abs/0809.4232

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arXiv