Martin compactification for discrete potential theory and the mean value property
type: Item
instance of: scholarly article
title: Martin compactification for discrete potential theory and the mean value property
zbMATH Open document ID: 0847.31004
DOI: 10.1007/BF01048068
author: Aurel Cornea
author: Jiří Veselý
published in: Potential Analysis
publication date: 1996-08-24T00:00:00Z
review text: Let \(h\) be a positive measurable function on a domain \(X\) in \(\mathbb{R}^n\). It is deduced, from many interesting results proved here, that if \(h\) satisfies a restricted mean-value property (i.e. the mean-value property at each point \(x\in X\) is satisfied for just one ball), then \(h\) is harmonic. Some related earlier investigations used probabilistic methods. Here the authors make use of a Martin-type compactification in the context of discrete potential theory.
Mathematics Subject Classification ID: 31B05
Mathematics Subject Classification ID: 31C20
Mathematics Subject Classification ID: 31A05
Mathematics Subject Classification ID: 31D05
Mathematics Subject Classification ID: 31C35
zbMATH DE Number: 826840
zbMATH Keywords: Martin boundary
zbMATH Keywords: restricted mean-value property
zbMATH Keywords: Martin-type compactification
reviewed by: Victor Anandam
MaRDI profile type: Publication
cites work: Ergodic Theory and Boundaries
cites work: Harmonic Functions and Mass Cancellation
cites work: Order and convexity in potential theory: H-cones. In collab. with Herbert Höllein
cites work: Potential theory. An analytic and probabilistic approach to balayage
cites work: Q4316863
cites work: Q5662251
cites work: Functions Possessing Restricted Mean Value Properties
cites work: A converse to the mean value theorem for harmonic functions
cites work: Q5581926
cites work: Q5512462
cites work: Q3874719
cites work: A zero-one law for a class of random walks and a converse to Gauss' mean value theorem
cites work: A Converse to the Mean Value Theorem for Harmonic Functions
full work available at URL: https://doi.org/10.1007/bf01048068
OpenAlex ID: W2042366778
description: scientific article; zbMATH DE number 826840