Uniform approximation and fine potential theory
type: Item
instance of: scholarly article
title: Uniform approximation and fine potential theory
zbMATH Open document ID: 0782.31002
author: S. Ladouceur
author: P. M. Gauthier
published in: Journal of Approximation Theory
publication date: 1993-06-29T00:00:00Z
review text: The following theorem is proved: Let \(F\) be a closed subset of \(\mathbb{R}^ N\), \(N\geq 2\). Then \(u\) belongs to the closure in the topology of uniform convergence on \(F\) of all harmonic functions on neighbourhoods of \(F\) if and only if \(u\) is continuous on \(F\) and \(u\) is finely harmonic on the fine interior on \(F\). The case of \(F\) being compact has been proved by \textit{A. Debiard} and \textit{B. Gaveau} see [J. Funct. Anal. 16, 289-304 (1974; Zbl 0297.31004)].
reviewed by: Ilpo Laine
Mathematics Subject Classification ID: 31B05
Mathematics Subject Classification ID: 31C40
zbMATH DE Number: 222121
zbMATH Keywords: topology of uniform convergence
zbMATH Keywords: fine interior
MaRDI profile type: Publication
full work available at URL: jath.1993.1011
OpenAlex ID: W2035307699
DOI: 10.1006/JATH.1993.1011
description: scientific article; zbMATH DE number 222121