Approximation of differentiation operators by bounded linear operators in Lebesgue spaces on the axis and related problems in the spaces of \((p,q)\)-multipliers and their predual spaces
type: Item
instance of: scholarly article
title: Approximation of differentiation operators by bounded linear operators in Lebesgue spaces on the axis and related problems in the spaces of \((p,q)\)-multipliers and their predual spaces
zbMATH Open document ID: 1542.41007
author: Vitalii Arestov
publication date: 2024-07-17T00:00:00Z
review text: In this article best approximations and operators that provide these best approximations are studied. The functions that are being approximated are univariate and are of certain smoothness classes, their derivatives being locally absolutely continuous and in some \(L^p\)-space.\N\NFor some given positive \(N\) we consider all operators \(T\) between such spaces with operator norm at most \(N\). We then look for the bounded linear operator(s) that give(s) the least error \(U(T)\) approximating a derivative of an approximand by the operator applied to functions whose \(n\)-derivatives have at lost \(L_p\)-norm one.\N\NThis is a Stechkin-type problem, and the paper provides solutions for this in some special cases.
reviewed by: Martin D. Buhmann
Mathematics Subject Classification ID: 41A17
Mathematics Subject Classification ID: 41A35
Mathematics Subject Classification ID: 41A44
zbMATH DE Number: 7882015
zbMATH Keywords: differentiation operator
zbMATH Keywords: Stechkin's problem
zbMATH Keywords: Kolmogorov inequality
zbMATH Keywords: \((p, q)\)-multiplier
zbMATH Keywords: predual space for space of \((p, q)\)-multipliers
MaRDI profile type: Publication
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published in: Ural mathematical journal
DOI: 10.15826/UMJ.2023.2.001
description: scientific article; zbMATH DE number 7882015