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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Volume 269, Pages 181–192 (Mi tm2893)  
This article is cited in 12 scientific papers (total in 12 papers)

On the reconstruction of convolution-type operators from inaccurate information

G. G. Magaril-Il'yaevab, K. Yu. Osipenkocb

a Moscow State Institute of Radio Engineering, Electronics and Automation (Technical University), Moscow, Russia
b Southern Mathematical Institute, Vladikavkaz Research Center, Russian Academy of Sciences, Vladikavkaz, Russia
c Russian State Technological University (MATI), Moscow, Russia
Full-text PDF (238 kB) Citations (12)
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Abstract: We address the problem of optimal reconstruction of the values of a linear operator on Rd or Zd from approximate values of other operators. Each operator acts as the multiplication of the Fourier transform by a certain function. As an application, we present explicit expressions for optimal methods of reconstructing the solution of the heat equation (for continuous and difference models) at a given instant of time from inaccurate measurements of this solution at other time instants.
Received in December 2009
English version:
Proceedings of the Steklov Institute of Mathematics, 2010, Volume 269, Pages 174–185
DOI: https://doi.org/10.1134/S008154381002015X
Bibliographic databases:
Document Type: Article
UDC: 517.51
Language: Russian
Citation: G. G. Magaril-Il'yaev, K. Yu. Osipenko, “On the reconstruction of convolution-type operators from inaccurate information”, Function theory and differential equations, Collected papers. Dedicated to Academician Sergei Mikhailovich Nikol'skii on the occasion of his 105th birthday, Trudy Mat. Inst. Steklova, 269, MAIK Nauka/Interperiodica, Moscow, 2010, 181–192; Proc. Steklov Inst. Math., 269 (2010), 174–185
Citation in format AMSBIB
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\paper On the reconstruction of convolution-type operators from inaccurate information
\inbook Function theory and differential equations
\bookinfo Collected papers. Dedicated to Academician Sergei Mikhailovich Nikol'skii on the occasion of his 105th birthday
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\vol 269
\pages 181--192
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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Linking options:
  • https://www.mathnet.ru/eng/tm2893
  • https://www.mathnet.ru/eng/tm/v269/p181
    • This publication is cited in the following 12 articles:
    1. 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  mathnet  crossref
    2. 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  mathnet  crossref
    3. E. V. Abramova, “Nailuchshee vosstanovlenie resheniya zadachi Dirikhle po netochno zadannomu spektru granichnoi funktsii”, Vladikavk. matem. zhurn., 19:4 (2017), 3–12  mathnet
    4. E. V. Abramova, “Vosstanovlenie resheniya zadachi Dirikhle po netochnym granichnym dannym”, Vladikavk. matem. zhurn., 17:1 (2015), 3–13  mathnet
    5. Bagramyan T.E., “on a Problem of Optimal Recovery and Kolmogorov Type Inequalities on An Interval”, J. Approx. Theory, 189 (2015), 160–169  crossref  mathscinet  zmath  isi  elib  scopus
    6. T. È. Bagramyan, “Optimal Recovery of Harmonic Functions in the Ball from Inaccurate Information on the Radon Transform”, Math. Notes, 98:2 (2015), 195–203  mathnet  crossref  crossref  mathscinet  isi  elib
    7. Zhang Y., Lukyanenko D.V., Yagola A.G., “An Optimal Regularization Method For Convolution Equations on the Sourcewise Represented Set”, J. Inverse Ill-Posed Probl., 23:5 (2015), 465–475  crossref  mathscinet  zmath  isi  elib  scopus
    8. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “On the best methods for recovering derivatives in Sobolev classes”, Izv. Math., 78:6 (2014), 1138–1157  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    9. G. G. Magaril-Il'yaev, K. Yu. Osipenko, E. O. Sivkova, “The best approximation of a set whose elements are known approximately”, J. Math. Sci., 218:5 (2016), 636–646  mathnet  crossref  mathscinet
    10. Bagramyan T.E., “Optimalnoe vosstanovlenie funktsii po netochno zadannomu preobrazovaniyu radona na klassakh, zadavaemykh stepenyu operatora laplasa”, Vestnik rossiiskogo universiteta druzhby narodov. seriya: matematika, informatika, fizika, 2013, no. 1, 19–25  elib
    11. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “On Optimal Recovery of Solutions to Difference Equations from Inaccurate Data”, J Math Sci, 189:4 (2013), 596  crossref
    12. T. E. Bagramyan, “Optimalnoe vosstanovlenie garmonicheskoi funktsii po netochno zadannym znacheniyam operatora radialnogo integrirovaniya”, Vladikavk. matem. zhurn., 14:1 (2012), 22–36  mathnet
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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