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Mat. Sb., 2012, Volume 203, Number 4, Pages 119–130 (Mi msb7903)  

This article is cited in 5 scientific papers (total in 5 papers)

Best recovery of the Laplace operator of a function from incomplete spectral data

G. G. Magaril-Il'yaeva, E. O. Sivkovab

a A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow
b Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)

Abstract: This paper is concerned with the problem of best recovery for a fractional power of the Laplacian of a smooth function on $\mathbb R^d$ from an exact or approximate Fourier transform for it, which is known on some convex subset of $\mathbb R^d$. A series of optimal recovery methods is constructed. Information about the Fourier transform outside some ball centred at the origin proves redundant — it is not used by the optimal methods. These optimal methods differ in the way they ‘process’ key information.
Bibliography: 12 titles.

Keywords: Laplace operator, optimal recovery, extremal problem, Fourier transform.

DOI: https://doi.org/10.4213/sm7903

Full text: PDF file (491 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2012, 203:4, 569–580

Bibliographic databases:

UDC: 517.518.1
MSC: 49N30, 35Q93
Received: 22.06.2011

Citation: G. G. Magaril-Il'yaev, E. O. Sivkova, “Best recovery of the Laplace operator of a function from incomplete spectral data”, Mat. Sb., 203:4 (2012), 119–130; Sb. Math., 203:4 (2012), 569–580

Citation in format AMSBIB
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\by G.~G.~Magaril-Il'yaev, E.~O.~Sivkova
\paper Best recovery of the Laplace operator of a~function from incomplete spectral data
\jour Mat. Sb.
\yr 2012
\vol 203
\issue 4
\pages 119--130
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\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2012SbMat.203..569M}
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\transl
\jour Sb. Math.
\yr 2012
\vol 203
\issue 4
\pages 569--580
\crossref{https://doi.org/10.1070/SM2012v203n04ABEH004235}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84862513198}


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  • https://doi.org/10.4213/sm7903
  • http://mi.mathnet.ru/eng/msb/v203/i4/p119

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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. E. O. Sivkova, “Ob optimalnom vosstanovlenii laplasiana funktsii po ee netochno zadannomu preobrazovaniyu Fure”, Vladikavk. matem. zhurn., 14:4 (2012), 63–72  mathnet
    2. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “On best harmonic synthesis of periodic functions”, J. Math. Sci., 209:1 (2015), 115–129  mathnet  crossref  mathscinet
    3. E. O. Sivkova, “Best recovery of the Laplace operator of a function and sharp inequalities”, J. Math. Sci., 209:1 (2015), 130–137  mathnet  crossref  mathscinet
    4. 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
    5. 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
  • Математический сборник Sbornik: Mathematics (from 1967)
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