Harmonic monsters.
type: Item
instance of: scholarly article
title: Harmonic monsters.
zbMATH Open document ID: 1054.30034
DOI: 10.1016/S0021-9045(03)00085-6
published in: Journal of Approximation Theory
publication date: 2003-07-30T00:00:00Z
review text: Using a theorem of \textit{S. J. Gardiner} [Harmonic approximation (1995; Zbl 0826.31002)], the author shows that there exists a harmonic function \(h\) on a non-empty open subset \(\Omega\) of \(\mathbb{R}^d\), where \(d\geq 2\), which behaves wildly near every boundary point of \(\Omega\). The function \(h\) is analogous to the holomorphic monster function of \textit{W. Luh} [J. Approximation Theory 53, No. 2, 128--144 (1988; Zbl 0669.30020)]. The author also compares his result with that of Luh's and obtains some improvements of his main result.
Mathematics Subject Classification ID: 30E10
Mathematics Subject Classification ID: 31B25
zbMATH DE Number: 1957011
zbMATH Keywords: universal harmonic approximation
author: D. H. Armitage
reviewed by: Yusuf Avci
MaRDI profile type: Publication
cites work: Harmonic analogues of G. R. MacLane's universal functions. II
cites work: Uniform and tangential harmonic approximation
cites work: Q4513495
cites work: Simplicial cones in potential theory. II: Approximation theorems
cites work: Q5568675
cites work: Superharmonic extension and harmonic approximation
cites work: Q4836158
cites work: Universal families and hypercyclic operators
cites work: Q4199010
cites work: Über cluster sets analytischer Funktionen
cites work: Universalfunktionen in einfach zusammenhängenden Gebieten
cites work: Holomorphic monsters
cites work: Multiply universal holomorphic functions
cites work: Q3128770
full work available at URL: s0021-9045(03)00085-6
OpenAlex ID: W2914140572
description: scientific article; zbMATH DE number 1957011