Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/111243
Title: Stechkin’s Problem on the Best Approximation of an Unbounded Operator by Bounded Ones and Related Problems
Other Titles: Задача Стечкина о наилучшем приближении неограниченного оператора ограниченными и родственные ей задачи
Authors: Arestov, V. V.
Akopyan, R. R.
Issue Date: 2020
Publisher: Krasovskii Institute of Mathematics and Mechanics
Krasovskii Institute of Mathematics and Mechanics UB RAS
Citation: Arestov V. V. Stechkin’s Problem on the Best Approximation of an Unbounded Operator by Bounded Ones and Related Problems [Задача Стечкина о наилучшем приближении неограниченного оператора ограниченными и родственные ей задачи] / V. V. Arestov, R. R. Akopyan // Trudy Instituta Matematiki i Mekhaniki UrO RAN. — 2020. — Vol. 26. — Iss. 4. — P. 7-31.
Abstract: This paper discusses Stechkin’s problem on the best approximation of a linear unbounded operator by bounded linear operators and related extremal problems. The main attention is paid to the approximation of differentiation operators in Lebesgue spaces on the axis and to the operator of the continuation of an analytic function to a domain from a part of the boundary of the domain. This is a review paper based on the materials of the authors’ lecture on September 14, 2020, at the X Internet video-conference “Day of Mathematics and Mechanics” of four institutes of the Russian Academy of Sciences: Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of RAS (Yekaterinburg), Sobolev Institute of the Siberian Branch of RAS (Novosibirsk), Steklov Mathematical Institute (Moscow), and the St. Petersburg Department of the Steklov Mathematical Institute. The lecture of the authors was dedicated to the 100th anniversary of the birth of Sergei Borisovich Stechkin. The problem of the best approximation of a linear unbounded operator by bounded ones is one of his legacies. We tried to at least partially reflect the new results, methods, and statements that appeared in this topic after the publication of the review papers (Arestov, Gabushin, 1995–1996). The material on this topic is wide; the selection of the material for the lecture and paper is the responsibility of the authors. © 2020 Krasovskii Institute of Mathematics and Mechanics. All rights reserved.
Keywords: ANALYTIC FUNCTIONS
BOUNDARY VALUES
DIFFERENTIATION OPERATOR
KOLMOGOROV INEQUALITY
RECOVERY
STECHKIN’S PROBLEM
UNBOUNDED LINEAR OPERATOR
URI: http://hdl.handle.net/10995/111243
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85103647219
PURE ID: 20233179
ISSN: 0134-4889
metadata.dc.description.sponsorship: This work was performed as a part of the research conducted in the Ural Mathematical Center and also supported by the Russian Foundation for Basic Research (project no. 18-01-00336) and by the Russian Academic Excellence Project (agreement no. 02.A03.21.0006 of August 27, 2013, between the Ministry of Education and Science of the Russian Federation and Ural Federal University).
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