Polynomial approximation in \(L_ p(S)\) for \(p>0\)
type: Item
instance of: scholarly article
title: Polynomial approximation in \(L_ p(S)\) for \(p>0\)
zbMATH Open document ID: 0870.41003
author: Z. Ditzian
published in: Constructive Approximation
publication date: 1997-09-08T00:00:00Z
review text: For a simple polytope \(S\) in \(R^d\) and \(p>0\), the author shows that the best possible approximation \(E_n (f)_p\leq Cw^r_S (f,1/n)_p\) where \(w^r_S (f,1/n)_p\) is a measure of smoothness of \(f\). The result is the best possible in the sense that a weak-type converse inequality is shown and a realization of \(w^r_S (f,t)_p\) via polynomial approximation is proved. A weaker inequality with \(1\leq p\leq\infty\), was proved in \textit{Z. Ditzian} and \textit{V. Totik} (Moduli of smoothness (1987; Zbl 0666.41001), Chapter 12). The above inequality for \(1\leq p \leq\infty\) is proved elsewhere by Z. Ditzian and K. Ivanov (manuscript).
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A17
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 922393
zbMATH Keywords: moduli of smoothness
zbMATH Keywords: realization
zbMATH Keywords: \(k\)-functionals
zbMATH Keywords: best possible approximation
reviewed by: H. P. Dikshit
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 922393