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Vladikavkazskii Matematicheskii Zhurnal, 2012, Volume 14, Number 1, Pages 22–36 (Mi vmj407)  
This article is cited in 5 scientific papers (total in 5 papers)

Optimal recovery of a harmonic function from inaccurate information on the values of the radial integration operator

T. Bagramyan

Peoples Friendship University of Russia, Moscow, Russia
Full-text PDF (650 kB) Citations (5)
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Abstract: We consider the problem of optimal recovery of a harmonic function in the unit ball from the inaccurate values of the radial integration operator. Information on the values of the operator is given as a function that differs from the exact values in the mean-square metric not more than a fixed error, either in the form of a finite set of Fourier coefficients calculated with a fixed error in the mean square or uniform metric.
Key words: optimal recovery, harmonic function, computerized tomography.
Received: 05.07.2011
Document Type: Article
UDC: 517.51
Language: Russian
Citation: T. Bagramyan, “Optimal recovery of a harmonic function from inaccurate information on the values of the radial integration operator”, Vladikavkaz. Mat. Zh., 14:1 (2012), 22–36
Citation in format AMSBIB
\Bibitem{Bag12}
\by T.~Bagramyan
\paper Optimal recovery of a~harmonic function from inaccurate information on the values of the radial integration operator
\jour Vladikavkaz. Mat. Zh.
\yr 2012
\vol 14
\issue 1
\pages 22--36
\mathnet{http://mi.mathnet.ru/vmj407}
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  • https://www.mathnet.ru/eng/vmj407
  • https://www.mathnet.ru/eng/vmj/v14/i1/p22
    • This publication is cited in the following 5 articles:
    1. T. Bagramyan, “Optimal inversion of the noisy Radon transform on classes defined by a degree of the Laplace operator”, J. Korea Soc. Ind. Appl. Math., 21:1 (2017), 29–37  crossref  mathscinet  zmath  isi
    2. T. Bagramyan, “The optimal recovery of a function from an inaccurate information on its k-plane transform”, Inverse Probl., 32:6 (2016), 065004  crossref  mathscinet  zmath  isi  scopus
    3. 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
    4. 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
    5. Bagramyan T.E., “Optimalnoe vosstanovlenie funktsii po ikh netochno zadannomu preobrazovaniyu radona”, Vestnik tambovskogo universiteta. seriya: estestvennye i tekhnicheskie nauki, 18:1 (2013), 15–17  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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