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Matematicheskie Zametki, 2024, Volume 115, Issue 6, Pages 807–824
DOI: https://doi.org/10.4213/mzm14168 (Mi mzm14168) 		 
Stechkin's Problem on the Approximation of the Differentiation Operator in the Uniform Norm on the Half-Line

R. R. Akopyana, V. V. Arestova, V. G. Timofeevb

a N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Saratov State University
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DOI: https://doi.org/10.4213/mzm14168
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.
Keywords: ideal spline, Landau–Kolmogorov inequality, best approximation of differentiation operators.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2024-1377
This work was performed at Ural Mathematical Center under the support of the Ministry of Science and Higher Education of the Russian Federation (contract no. 075-02-2024-1377).
Received: 06.10.2023
English version:
Mathematical Notes, 2024, Volume 115, Issue 6, Pages 853–867
DOI: https://doi.org/10.1134/S0001434624050225
Bibliographic databases:
Document Type: Article
UDC: 517
MSC: 26D10, 47A58
Language: Russian
Citation: R. R. Akopyan, V. V. Arestov, V. G. Timofeev, “Stechkin's Problem on the Approximation of the Differentiation Operator in the Uniform Norm on the Half-Line”, Mat. Zametki, 115:6 (2024), 807–824; Math. Notes, 115:6 (2024), 853–867
Citation in format AMSBIB
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\paper Stechkin's Problem on the Approximation of the Differentiation Operator in the Uniform Norm on the Half-Line
\jour Mat. Zametki
\yr 2024
\vol 115
\issue 6
\pages 807--824
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\crossref{https://doi.org/10.4213/mzm14168}
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\transl
\jour Math. Notes
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\issue 6
\pages 853--867
\crossref{https://doi.org/10.1134/S0001434624050225}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85198655781}
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