Discontinuity of best harmonic approximants
type: Item
instance of: scholarly article
title: Discontinuity of best harmonic approximants
zbMATH Open document ID: 0920.41015
published in: Journal of Approximation Theory
publication date: 1999-05-31T00:00:00Z
review text: Let \(D\) be a (Jordan) domain in \(\mathbb{R}^2\) and \(f\) some real-valued and bounded continuous function on \(\overline D\). Then \(f\) has some best harmonic approximant \(h:D\in\mathbb{R}\) in the sense of uniform approximation on \(D\), but it is known that \(h\) must not have a continuous extension on \(\overline D\). The authors present very concrete examples as well as classes of real analytic \(f\) showing this phenomenon.
reviewed by: Gerald Schmieder
Mathematics Subject Classification ID: 41A50
Mathematics Subject Classification ID: 31A05
zbMATH DE Number: 1271289
zbMATH Keywords: best harmonic approximation
author: David A. Legg
author: Yifei Pan
MaRDI profile type: Publication
cites work: Q4137585
cites work: Best uniform approximation by harmonic functions on subsets of Riemannian manifolds
cites work: Q3327087
cites work: Q4001917
cites work: A counterexample in the theory of best approximation
description: scientific article; zbMATH DE number 1271289