Stechkin’s Problem on Approximation of the Differentiation Operator in the Uniform Norm on the Half-Line

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-07-15 DOI:10.1134/s0001434624050225

R. R. Akopyan, V. V. Arestov, V. G. Timofeev

引用次数: 0

Abstract

Stechkin’s problem of the best approximation of differentiation operators by bounded linear operators on the half-line in the uniform norm is studied. The structure of the best approximation operator is investigated, and its relationship to the spline dual (in the sense of N. P. Kuptsov) to the extremal spline in the Landau–Kolmogorov inequality on the half-line is examined.

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斯泰奇金关于半线上均匀规范微分算子的逼近问题

摘要研究了斯泰奇金提出的用均匀规范半线上的有界线性算子对微分算子进行最佳逼近的问题。研究了最佳近似算子的结构，并探讨了它与半线上的 Landau-Kolmogorov 不等式中极值样条的对偶（N. P. Kuptsov 意义上的）样条的关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.