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.
\Bibitem{MagSiv19}
\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
\mathnet{http://mi.mathnet.ru/emj349}
\crossref{https://doi.org/10.32523/2077-9879-2019-10-4-75-84}
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Linking options:
https://www.mathnet.ru/eng/emj349
https://www.mathnet.ru/eng/emj/v10/i4/p75
This publication is cited in the following 11 articles:
E. V. Abramova, E. O. Sivkova, “On the Optimal Recovery of One Family of Operators on a Class of Functions from Approximate Information about Its Spectrum”, Sib Math J, 65:2 (2024), 245
E. O. Sivkova, “Optimal Recovery of a Family of Operators from Inaccurate Measurements on a Compact Set”, Sib Math J, 65:2 (2024), 495
E. V. Abramova, E. O. Sivkova, “O nailuchshem vosstanovlenii semeistva operatorov na klasse funktsii po netochno zadannomu ikh spektru”, Vladikavk. matem. zhurn., 26:1 (2024), 13–26
E. V. Abramova, E. O. Sivkova, “Ob optimalnom vosstanovlenii odnogo semeistva operatorov na klasse funktsii po priblizhennoi informatsii ob ikh spektre”, Sib. matem. zhurn., 65:2 (2024), 235–248
M. V. Polovinkina, “On the Recovery of Semi-group Operators in Weight Spaces from Incomplete and Inaccurate Data”, Lobachevskii J Math, 45:11 (2024), 5658
E. V. Abramova, E. O. Sivkova, “Optimalnoe vosstanovlenie resheniya zadachi Dirikhle dlya poluploskosti”, Sib. matem. zhurn., 64:3 (2023), 441–449
E. O. Sivkova, “Optimalnoe vosstanovlenie semeistva operatorov po netochnym izmereniyam na kompakte”, Vladikavk. matem. zhurn., 25:2 (2023), 124–135
G. G. Magaril-Il'yaev, E. O. Sivkova, “On the Best Recovery of a Family of Operators on the Manifold Rn×Tm”, Proc. Steklov Inst. Math., 323 (2023), 188–196
E. V. Abramova, E. O. Sivkova, “Optimal Recovery of the Solution to the Dirichlet Problem in the Half-Plane”, Sib Math J, 64:3 (2023), 507
G. G. Magaril-Il'yaev, K. Yu. Osipenko, E. O. Sivkova, “Optimal Recovery of Pipe Temperature from Inaccurate Measurements”, Proc. Steklov Inst. Math., 312 (2021), 207–214
E. V. Abramova, G. G. Magaril-Il'yaev, E. O. Sivkova, “Best recovery of the solution of the Dirichlet problem in a half-space from inaccurate data”, Comput. Math. Math. Phys., 60:10 (2020), 1656–1665
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