Approximation by harmonic functions in the \(C^m\)-norm and harmonic \(C^m\)-capacity of compact sets in \(\mathbb{R}^n\)
type: Item
instance of: scholarly article
title: Approximation by harmonic functions in the \(C^m\)-norm and harmonic \(C^m\)-capacity of compact sets in \(\mathbb{R}^n\)
zbMATH Open document ID: 0921.41010
DOI: 10.1007/BF02360872
author: Yu. A. Gorokhov
published in: Mathematical Notes
publication date: 1999-09-30T00:00:00Z
review text: The author studies the function \(\Lambda^m(X)\), \(0< m<1\), of compact sets \(X\) in \(\mathbb{R}^n\), \(n\geq 2\), defined as the distance in the space \(C^m(X)\equiv \text{lip}^m(X)\) from the function \(| x|^2\) to the subspace \(H^m(X)\) which is the closure in \(C^m(X)\) of the class of functions harmonic in the neighborhood of \(X\). Among other results, it is proven that the conditions \(\Lambda^m(X)= 0\) and \(C^m(X)= H^m(X)\) are equivalent.
Mathematics Subject Classification ID: 41A30
Mathematics Subject Classification ID: 31B05
Mathematics Subject Classification ID: 30E10
zbMATH DE Number: 1257035
zbMATH Keywords: harmonic function
zbMATH Keywords: harmonic capacities
reviewed by: Yusuf Avci
MaRDI profile type: Publication
cites work: On uniform approximation by harmonic functions
cites work: Q5607484
cites work: $ C^m$-APPROXIMATIONS BY HARMONIC POLYNOMIALS ON COMPACT SETS IN $ \mathbb{R}^n$
cites work: Q5539857
cites work: Q4713874
description: scientific article; zbMATH DE number 1257035