The characterization of the derivatives for linear combinations of Post-Widder operators in \(L_p\)
type: Item
instance of: scholarly article
title: The characterization of the derivatives for linear combinations of Post-Widder operators in \(L_p\)
zbMATH Open document ID: 0944.41010
author: Song Li
author: Ren Tai Wang
published in: Journal of Approximation Theory
publication date: 2000-09-17T00:00:00Z
review text: The Post-Widder operators constitue inversion formulas for the Laplace transform. \textit{Z. Ditzian} and \textit{V. Totik} [Modulus of smoothness (1987; Zbl 0666.41001)] proved direct and converse results for the rates of convergence for certain linear combinations of Post-Widder operators. The theorems relate the convergence of the operators with a modulus of smoothness of the function. Among other results, this detailed work extends the Ditzian-Totik results to characterize the global rate of weighted \(L_p\) \(( 1\leq p\leq \infty)\) approximation of derivatives by corresponding derivatives of linear combinations of Post-Widder operators.
Mathematics Subject Classification ID: 41A35
Mathematics Subject Classification ID: 41A25
zbMATH DE Number: 1278843
zbMATH Keywords: rate of convergence
zbMATH Keywords: modulus of smoothness
reviewed by: Daniel Wulbert
MaRDI profile type: Publication
full work available at URL: jath.1997.3275
OpenAlex ID: W2055486867
cites work: Q3817079
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cites work: Equivalence theorem on weighted simultaneous \(L_ p\)-approximation by the method of Kantorovič operators
cites work: On a paper of Mazhar and Totik
cites work: On smoothness characterized by Bernstein type operators
DOI: 10.1006/JATH.1997.3275
description: scientific article; zbMATH DE number 1278843