On weak Chebyshev subspaces. I. Equioscillation of the error in approximation

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Abstract

This paper is a generalization of the result obtained by F. Deutsch, G. Nürnberger, and I. Singer (1980, Pacific J. Math. 88, 9-31). It is shown that if Q is a locally compact totally ordered space, and N is an n-dimensional subspace of C0(Q), then N is a weak Chebyshev subspace if and only if for each f ε{lunate} C0(Q), there is g ε{lunate} N such that ∥f - g∥ = d(f, N) and (f - g) equioscillates at (n + 1) points.

Original languageEnglish
Pages (from-to)129-141
Number of pages13
JournalJournal of Approximation Theory
Volume67
Issue number2
DOIs
Publication statusPublished - 1991

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ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Mathematics(all)
  • Applied Mathematics

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