Boundary behaviour of λ-polyharmonic functions on regular trees

Ecaterina Sava-Huss; Wolfgang Woess

doi:10.1007/s10231-020-00981-8

Boundary behaviour of λ-polyharmonic functions on regular trees

Ecaterina Sava-Huss^*, Wolfgang Woess

^*Corresponding author for this work

Institute of Discrete Mathematics (5050)

Research output: Contribution to journal › Article › peer-review

Abstract

This paper studies the boundary behaviour of λ-polyharmonic functions for the simple random walk operator on a regular tree, where λ is complex and |λ>ρ, the ℓ2-spectral radius of the random walk. In particular, subject to normalisation by spherical, resp. polyspherical functions, Dirichlet and Riquier problems at infinity are solved, and a non-tangential Fatou theorem is proved.

Original language	English
Pages (from-to)	35-50
Number of pages	16
Journal	Annali di Matematica Pura ed Applicata
Volume	200
Issue number	1
DOIs	https://doi.org/10.1007/s10231-020-00981-8
Publication status	Published - Feb 2021

Keywords

Dirichlet and Riquier problems at infinity
Fatou theorem
Regular tree
Simple random walk
λ-polyharmonic functions

ASJC Scopus subject areas

Applied Mathematics

Fields of Expertise

Information, Communication & Computing

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10.1007/s10231-020-00981-8Licence: CC BY 4.0

Cite this

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title = "Boundary behaviour of λ-polyharmonic functions on regular trees",

abstract = "This paper studies the boundary behaviour of λ-polyharmonic functions for the simple random walk operator on a regular tree, where λ is complex and |λ>ρ, the ℓ2-spectral radius of the random walk. In particular, subject to normalisation by spherical, resp. polyspherical functions, Dirichlet and Riquier problems at infinity are solved, and a non-tangential Fatou theorem is proved.",

keywords = "Dirichlet and Riquier problems at infinity, Fatou theorem, Regular tree, Simple random walk, λ-polyharmonic functions",

author = "Ecaterina Sava-Huss and Wolfgang Woess",

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AB - This paper studies the boundary behaviour of λ-polyharmonic functions for the simple random walk operator on a regular tree, where λ is complex and |λ>ρ, the ℓ2-spectral radius of the random walk. In particular, subject to normalisation by spherical, resp. polyspherical functions, Dirichlet and Riquier problems at infinity are solved, and a non-tangential Fatou theorem is proved.

KW - Dirichlet and Riquier problems at infinity

KW - Fatou theorem

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KW - Simple random walk

KW - λ-polyharmonic functions

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ER -

Boundary behaviour of λ-polyharmonic functions on regular trees

Abstract

Keywords

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