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Mat. Zametki, 2015, Volume 98, Issue 2, Pages 163–172 (Mi mz9680)  

This article is cited in 2 scientific papers (total in 2 papers)

Optimal Recovery of Harmonic Functions in the Ball from Inaccurate Information on the Radon Transform

T. È. Bagramyan

Peoples Friendship University of Russia, Moscow

Abstract: We consider the problem of the optimal recovery of harmonic functions in the ball from inaccurate information on the Radon transform. Presented are the error of the optimal recovery and the set of optimal methods for which this error is attained.

Keywords: optimal recovery, Radon transform, harmonic function, Hardy space, Gegenbauer polynomial, spherical harmonic, Lagrange function, Bessel function.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00456
This work was supported by the Russian Foundation for Basic Research (grant no. 14-01-00456).


DOI: https://doi.org/10.4213/mzm9680

Full text: PDF file (489 kB)
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English version:
Mathematical Notes, 2015, 98:2, 195–203

Bibliographic databases:

UDC: 517.5
Received: 20.05.2012

Citation: T. È. Bagramyan, “Optimal Recovery of Harmonic Functions in the Ball from Inaccurate Information on the Radon Transform”, Mat. Zametki, 98:2 (2015), 163–172; Math. Notes, 98:2 (2015), 195–203

Citation in format AMSBIB
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\by T.~\`E.~Bagramyan
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\jour Mat. Zametki
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  • https://doi.org/10.4213/mzm9680
  • http://mi.mathnet.ru/eng/mz/v98/i2/p163

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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  elib  scopus
    2. 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
  • Математические заметки Mathematical Notes
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