Bounded harmonic functions for the Heckman--Opdam Laplacian

Details Bounded harmonic functions for the Heckman--Opdam Laplacian Bounded harmonic functions for the Heckman--Opdam Laplacian

2008-09-24

arxiv.org/abs/0809.4232v2

Mathematics

Probability

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

Scientific paper

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.

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