Unicity subspaces in \(L^ 1\)-approximation
type: Item
instance of: scholarly article
title: Unicity subspaces in \(L^ 1\)-approximation
zbMATH Open document ID: 0603.41019
DOI: 10.1016/0021-9045(86)90007-9
author: Allan Pinkus
published in: Journal of Approximation Theory
publication date: 1986-01-01T00:00:00Z
review text: Let U be an n-dimensional subspace of C[0,1]. U is an \(L^ 1_ w\)- unicity space if to each \(f\in C[0,1]\) there exists a unique best approximant from U to f in the \(L^ 1_ w\)-norm, where w is a positive continuous function and \(\| f\|_ w=\int^{1}_{0}| f(x)| w(x) dx.\) The characterization of unicity spaces is w dependent. This paper totally characterizes all subspaces U which are unicity spaces for all w as above.
Mathematics Subject Classification ID: 41A52
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A65
zbMATH DE Number: 3973498
zbMATH Keywords: WT-system
zbMATH Keywords: \(L^ 1_ w\)-unicity space
MaRDI profile type: Publication
full work available at URL: 0021-9045(86)90007-9
OpenAlex ID: W2012566694
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description: scientific article; zbMATH DE number 3973498