\(L^{1}\)-approximation and finding solutions with small support
type: Item
instance of: scholarly article
title: \(L^{1}\)-approximation and finding solutions with small support
zbMATH Open document ID: 1262.41017
author: Yoav Benyamini
author: András Kroó
author: Allan Pinkus
published in: Constructive Approximation
publication date: 2013-01-30T00:00:00Z
review text: As noted in the abstract, ``for many subspaces \(M\), there exist \(\alpha^*(M)>0\) with the following property: if \(f\) vanishes off a set of measure at most \(\alpha^*(M)\), then the zero function is a best \(L^1\)-approximant to \(f\) from \(M\).'' The authors explain this phenomenon, starting with the characterization of the best approximation from a linear subspace in the \(L^1\)-norm. Several specific examples of subspaces, with lower bounds and sometimes upper bounds on the associated \(\alpha^*(M)\) are given. Finally, the authors present some open questions.
Mathematics Subject Classification ID: 41A50
Mathematics Subject Classification ID: 41A17
zbMATH DE Number: 6132834
zbMATH Keywords: \(L^{1}\)-approximation
zbMATH Keywords: Nikolskii-type inequalities
zbMATH Keywords: sparsest solutions
zbMATH Keywords: best approximation
zbMATH Keywords: minimal support
reviewed by: Yuri A. Farkov
MaRDI profile type: Publication
full work available at URL: s00365-011-9150-y
OpenAlex ID: W2169886066
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DOI: 10.1007/S00365-011-9150-Y
description: scientific article; zbMATH DE number 6132834