Displaying similar documents to “Boundary behaviour of eigenfunctions of the Laplace operator on trees”

Local admissible convergence of harmonic functions on non-homogeneous trees

Massimo A. Picardello (2010)

Colloquium Mathematicae

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We prove admissible convergence to the boundary of functions that are harmonic on a subset of a non-homogeneous tree equipped with a transition operator that satisfies uniform bounds suitable for transience. The approach is based on a discrete Green formula, suitable estimates for the Green and Poisson kernel and an analogue of the Lusin area function.

Poisson kernels of drifted Laplace operators on trees and on the half-plane

Enrico Casadio Tarabusi, Alessandro Figà-Talamanca (2010)

Colloquium Mathematicae

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Starting with the computation of the appropriate Poisson kernels, we review, complement, and compare results on drifted Laplace operators in two different contexts: homogeneous trees and the hyperbolic half-plane.

Asymptotic properties of harmonic measures on homogeneous trees

Konrad Kolesko (2010)

Colloquium Mathematicae

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Let Aff(𝕋) be the group of isometries of a homogeneous tree 𝕋 fixing an end of its boundary. Given a probability measure on Aff(𝕋) we consider an associated random process on the tree. It is known that under suitable hypothesis this random process converges to the boundary of the tree defining a harmonic measure there. In this paper we study the asymptotic behaviour of this measure.