English

Bounded harmonic functions for the Heckman--Opdam Laplacian

Probability 2008-10-21 v2 Classical Analysis and ODEs

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.

Keywords

Cite

@article{arxiv.0809.4232,
  title  = {Bounded harmonic functions for the Heckman--Opdam Laplacian},
  author = {Bruno Schapira},
  journal= {arXiv preprint arXiv:0809.4232},
  year   = {2008}
}

Comments

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

R2 v1 2026-06-21T11:23:49.290Z