This paper studies potential theory on treebolic space, that is, the horocyclic product of a regular tree and hyperbolic upper half plane. Relying on the analysis on strip complexes developed by the authors, a family of Laplacians with “vertical drift” parameters is considered. We investigate the positive harmonic functions associated with those Laplacians.
Brownian motion on treebolic space : positive harmonic functions / A. Bendikov, L. Saloff-Coste, M. Salvatori, W. Woess. - In: ANNALES DE L'INSTITUT FOURIER. - ISSN 1777-5310. - 66:4(2016), pp. 1691-1731.
Brownian motion on treebolic space : positive harmonic functions
M. Salvatori;
2016
Abstract
This paper studies potential theory on treebolic space, that is, the horocyclic product of a regular tree and hyperbolic upper half plane. Relying on the analysis on strip complexes developed by the authors, a family of Laplacians with “vertical drift” parameters is considered. We investigate the positive harmonic functions associated with those Laplacians.
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