Boundary behaviour of [Formula: see text] -polyharmonic functions on regular trees

This paper studies the boundary behaviour of [Formula: see text] -polyharmonic functions for the simple random walk operator on a regular tree, where [Formula: see text] is complex and [Formula: see text] , the [Formula: see text] -spectral radius of the random walk. In particular, subject to normal...

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Autores principales: Sava-Huss, Ecaterina, Woess, Wolfgang
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7851043/
https://www.ncbi.nlm.nih.gov/pubmed/33568883
http://dx.doi.org/10.1007/s10231-020-00981-8
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author Sava-Huss, Ecaterina
Woess, Wolfgang
author_facet Sava-Huss, Ecaterina
Woess, Wolfgang
author_sort Sava-Huss, Ecaterina
collection PubMed
description This paper studies the boundary behaviour of [Formula: see text] -polyharmonic functions for the simple random walk operator on a regular tree, where [Formula: see text] is complex and [Formula: see text] , the [Formula: see text] -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.
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spelling pubmed-78510432021-02-08 Boundary behaviour of [Formula: see text] -polyharmonic functions on regular trees Sava-Huss, Ecaterina Woess, Wolfgang Ann Mat Pura Appl Article This paper studies the boundary behaviour of [Formula: see text] -polyharmonic functions for the simple random walk operator on a regular tree, where [Formula: see text] is complex and [Formula: see text] , the [Formula: see text] -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. Springer Berlin Heidelberg 2020-04-29 2021 /pmc/articles/PMC7851043/ /pubmed/33568883 http://dx.doi.org/10.1007/s10231-020-00981-8 Text en © The Author(s) 2020 Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Article
Sava-Huss, Ecaterina
Woess, Wolfgang
Boundary behaviour of [Formula: see text] -polyharmonic functions on regular trees
title Boundary behaviour of [Formula: see text] -polyharmonic functions on regular trees
title_full Boundary behaviour of [Formula: see text] -polyharmonic functions on regular trees
title_fullStr Boundary behaviour of [Formula: see text] -polyharmonic functions on regular trees
title_full_unstemmed Boundary behaviour of [Formula: see text] -polyharmonic functions on regular trees
title_short Boundary behaviour of [Formula: see text] -polyharmonic functions on regular trees
title_sort boundary behaviour of [formula: see text] -polyharmonic functions on regular trees
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7851043/
https://www.ncbi.nlm.nih.gov/pubmed/33568883
http://dx.doi.org/10.1007/s10231-020-00981-8
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AT woesswolfgang boundarybehaviourofformulaseetextpolyharmonicfunctionsonregulartrees

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