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Eurasian Mathematical Journal, 2019, Volume 10, Number 4, Pages 75–84
DOI: https://doi.org/10.32523/2077-9879-2019-10-4-75-84 (Mi emj349) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Optimal recovery of semi-group operators from inaccurate data

G. G. Magaril-Il'yaevab, E. O. Sivkovacd

a Institute for Information Transmission Problems, Russian Academy of Sciences, Bol'shoi Karetnyi per. 19, str. 1, Moscow, 127051 Russia
b Southern Mathematical Institute — the Affiliate of the Vladikavkaz Scientific Centre of the Russian Academy of Sciences, ul. Vatutina 53, Vladikavkaz, 362025 Russia
c Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991 Russia
d Moscow Pedagogical State University (MPGU), 1/1 M. Pirogovskaya St, Moscow, 119991 Russia
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DOI: https://doi.org/10.32523/2077-9879-2019-10-4-75-84
Abstract: The problem of optimal recovery of the operator at a given value of the parameter from inaccurate information about the other parameters is solved for a special one-parameter semi-group of operators. A family of optimal recovery methods is constructed. As a corollary, we obtain families of optimal recovery methods in the problem of recovery of a solution of the heat equation on the line and in the problem of recovery of a solution to the Dirichlet problem for the half-plane.
Keywords and phrases: semi-group of operators, optimal recovery, extremal problem, Fourier transform.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00649_a
This work was supported by the Russian Foundation for Basic Research, project no. 17-01-00649-a.
Received: 01.03.2019
Bibliographic databases:
Document Type: Article
MSC: 39B62, 42B10, 49K35
Language: English
Citation: G. G. Magaril-Il'yaev, E. O. Sivkova, “Optimal recovery of semi-group operators from inaccurate data”, Eurasian Math. J., 10:4 (2019), 75–84
Citation in format AMSBIB
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\by G.~G.~Magaril-Il'yaev, E.~O.~Sivkova
\paper Optimal recovery of semi-group operators from inaccurate data
\jour Eurasian Math. J.
\yr 2019
\vol 10
\issue 4
\pages 75--84
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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