Bounded harmonic functions for the Heckman--Opdam Laplacian
Bruno Schapira (LM-Orsay)
TL;DR
This paper characterizes the set of bounded harmonic functions for the Heckman--Opdam Laplacian with multiplicity greater than 1/2, revealing its structure and implications for hypergeometric functions.
Contribution
It provides a complete description of bounded harmonic functions for the Heckman--Opdam Laplacian in a specific parameter regime, linking harmonic analysis and special functions.
Findings
The set of bounded harmonic functions forms a vector space of dimension equal to the Weyl group cardinality.
The results have implications for the properties of associated hypergeometric functions.
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.
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Taxonomy
TopicsGeometry and complex manifolds · Spectral Theory in Mathematical Physics · Quantum chaos and dynamical systems