Effective moduli from ineffective uniqueness proofs. An unwinding of de La Vallée Poussin's proof for Chebycheff approximation
type: Item
instance of: scholarly article
title: Effective moduli from ineffective uniqueness proofs. An unwinding of de La Vallée Poussin's proof for Chebycheff approximation
zbMATH Open document ID: 0795.03086
DOI: 10.1016/0168-0072(93)90213-W
author: Ulrich Kohlenbach
published in: Annals of Pure and Applied Logic
publication date: 1994-09-01T00:00:00Z
review text: The paper deals with the search for effective moduli from ineffective uniqueness proofs of classical analysis. The author shows that, under suitable conditions, it is possible to extract an effective modulus of uniqueness from the proof. In particular this applies to the proof of uniqueness for the best Chebycheff approximation of \(f\in{\mathcal C}[0,1]\) by polynomials of degree \(\leq n\) given by de La Vallée Poussin, and provides explicit moduli of uniqueness and uniform constants of strong unicity.
Mathematics Subject Classification ID: 03F60
Mathematics Subject Classification ID: 26E40
zbMATH DE Number: 444823
zbMATH Keywords: ineffective uniqueness proofs of classical analysis
zbMATH Keywords: effective modulus of uniqueness
zbMATH Keywords: Chebycheff approximation
reviewed by: Pier Luigi Ferrari
MaRDI profile type: Publication
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full work available at URL: 0168-0072(93)90213-w
OpenAlex ID: W2061466015
description: scientific article; zbMATH DE number 444823