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Mat. Zametki, 2012, Volume 92, Issue 1, Pages 59–67 (Mi mz9042)  

This article is cited in 6 scientific papers (total in 6 papers)

How Best to Recover a Function from Its Inaccurately Given Spectrum?

G. G. Magaril-Il'yaev, K. Yu. Osipenko

A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow

Abstract: Consider the problem of optimal recovery of a function and its derivatives on the line from the Fourier transform of the function known approximately on a set of finite measure. We find an optimal recovery method and an optimal set on which we must measure the Fourier transform with given error.

Keywords: optimal recovery of a function, Fourier transform, Sobolev class of functions, Lagrange function

DOI: https://doi.org/10.4213/mzm9042

Full text: PDF file (501 kB)
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English version:
Mathematical Notes, 2012, 92:1, 51–58

Bibliographic databases:

UDC: 517.984.64
Received: 17.11.2010

Citation: G. G. Magaril-Il'yaev, K. Yu. Osipenko, “How Best to Recover a Function from Its Inaccurately Given Spectrum?”, Mat. Zametki, 92:1 (2012), 59–67; Math. Notes, 92:1 (2012), 51–58

Citation in format AMSBIB
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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. 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
    2. K. Yu. Osipenko, “Optimal recovery of linear operators in non-Euclidean metrics”, Sb. Math., 205:10 (2014), 1442–1472  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. 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
    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. Osipenko K.Yu., “Optimal Recovery of Operators and Multidimensional Carlson Type Inequalities”, J. Complex., 32:1 (2016), 53–73  crossref  mathscinet  zmath  isi
    6. S. A. Unuchek, “Vosstanovlenie operatorov razdelennoi raznosti netochno zadannoi posledovatelnosti po ee preobrazovaniyu Fure”, Vladikavk. matem. zhurn., 20:3 (2018), 94–104  mathnet  crossref
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