Recent developments in harmonic approximation, with applications
type: Item
instance of: scholarly article
title: Recent developments in harmonic approximation, with applications
zbMATH Open document ID: 0859.31001
DOI: 10.1007/BF03322201
published in: Results in Mathematics
publication date: 1997-04-07T00:00:00Z
review text: The authors survey developments in the field of uniform and tangential (with a given error function) harmonic approximation. Starting point is a theorem of \textit{J. L. Walsh} [Bull. Am. Math. Soc., II. Ser. 35, 499-544 (1929; JFM 55.0889.05)], which says that every function harmonic in a neighborhood of a compact subset \(E\) of \(\mathbb{R}^n\) with connected complement can be uniformly approximated on \(E\) by functions harmonic on the whole of \(\mathbb{R}^n\). The authors present some recent extensions of this result in which approximation takes place on closed sets and they give several applications concerning universal functions, the Radon transform, the maximum principle, and the Dirichlet problem.
Mathematics Subject Classification ID: 31-02
Mathematics Subject Classification ID: 31B05
Mathematics Subject Classification ID: 30E10
Mathematics Subject Classification ID: 41-02
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 872695
zbMATH Keywords: harmonic functions
zbMATH Keywords: tangential harmonic approximation
zbMATH Keywords: JFM 55.0889.05
zbMATH Keywords: universal functions
zbMATH Keywords: Radon transform
zbMATH Keywords: maximum principle
zbMATH Keywords: Dirichlet problem
author: D. H. Armitage
author: P. M. Gauthier
reviewed by: Klaus Menke
MaRDI profile type: Publication
cites work: Better than Uniform Approximation on Closed Sets by Harmonic Functions with Singularities
cites work: Nonuniqueness for the Radon Transform
cites work: Tangential Harmonic Approximation on Relatively Closed Sets
cites work: Q4023465
cites work: Q5840466
cites work: A Maximum Principle for Subharmonic and Plurisubharmonic Functions
cites work: The Dirichlet problem with non-compact boundary
cites work: Q4836158
cites work: Q4309441
cites work: Uniform Approximation on Unbounded Sets by Harmonic Functions with Logarithmic Singularities
cites work: Uniform Approximation on Closed Sets by Harmonic Functions with Newtonian Singularities
cites work: Asymptotic Maximum Principles for Subharmonic and Plurisubharmonic Functions
cites work: Elliptic Partial Differential Equations of Second Order
cites work: The Radon transform
cites work: Q5581926
cites work: Uniform And Tangential Approximations By Meromorphic Functions on Closed Sets
cites work: Uniqueness and Nonuniqueness for the Radon Transform
description: scientific article; zbMATH DE number 872695