Singular numbers of the imbedding operators for certain classes of analytic and harmonic functions
type: Item
instance of: scholarly article
title: Singular numbers of the imbedding operators for certain classes of analytic and harmonic functions
zbMATH Open document ID: 0628.30050
DOI: 10.1007/BF01104867
author: O. G. Parfenov
published in: Journal of Soviet Mathematics
publication date: 1986-01-01T00:00:00Z
review text: Let G and g be bounded simply connected domains whose boundaries are rectifiable Jordan curves and \(\bar g\subset G\). Let \(\lambda\),\(\mu\) be finite Borel measures defined on \(\bar G\) and \(\bar g,\) respectively. By \(A^ 2(G,\lambda)\) (respectively: \(h^ 2(G,\lambda))\) is denoted the closure in \(L^ 2(G,\lambda)\) of all functions analytic (resp. harmonic) in G. There is studied the best approximation in the mean of functions under consideration by estimations of s-numbers of embedding operators \[ I: A^ 2(G,\lambda)\to L_ 2(g,\mu),\quad I f=f|_ g, \] \[ I_ h: h^ 2(G,\lambda)\to L_ 2(g,\mu),\quad I_ hf=f|_ g, \] provided that they are compact. Remark of the reviewer: The language of the paper seems to be rather strange: it is a so-called dictionary translation (for instance: ``circumstance'' instead of ``neighbourhood'').
Mathematics Subject Classification ID: 30H05
Mathematics Subject Classification ID: 46E20
Mathematics Subject Classification ID: 47B10
zbMATH DE Number: 4021560
zbMATH Keywords: spaces of harmonic functions
zbMATH Keywords: best approximation
zbMATH Keywords: s-numbers
zbMATH Keywords: embedding operators
reviewed by: Danuta Przeworska-Rolewicz
MaRDI profile type: Publication
cites work: Q5571194
cites work: Q5574105
cites work: Q3927741
cites work: Q3949270
cites work: The n-width of sets of analytic functions
cites work: Q3247378
description: scientific article; zbMATH DE number 4021560