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Mat. Sb., 2004, Volume 195, Number 10, Pages 67–82 (Mi msb853)  

This article is cited in 9 scientific papers (total in 9 papers)

Optimal recovery of values of functions and their derivatives from inaccurate data on the Fourier transform

G. G. Magaril-Il'yaeva, K. Yu. Osipenkob

a Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)
b Moscow State Aviation Technological University

Abstract: The problems of the optimal recovery of the derivatives of functions from inaccurate information about the Fourier transforms of these functions on a finite interval or the entire number line are considered. The Stechkin problem of the approximation of derivatives by bounded linear functionals, which is closely connected to this range of problems, is also studied. Precise Kolmogorov-type inequalities for derivatives corresponding to these problems are obtained.

DOI: https://doi.org/10.4213/sm853

Full text: PDF file (303 kB)
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English version:
Sbornik: Mathematics, 2004, 195:10, 1461–1476

Bibliographic databases:

UDC: 517.5
MSC: Primary 41A65; Secondary 41A46
Received: 26.02.2004

Citation: G. G. Magaril-Il'yaev, K. Yu. Osipenko, “Optimal recovery of values of functions and their derivatives from inaccurate data on the Fourier transform”, Mat. Sb., 195:10 (2004), 67–82; Sb. Math., 195:10 (2004), 1461–1476

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. E. V. Vvedenskaya, K. Yu. Osipenko, “Discrete Analogs of Taikov's Inequality and Recovery of Sequences Given with an Error”, Math. Notes, 92:4 (2012), 473–484  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. N. Temirgaliev, K. E. Sherniyazov, M. E. Berikhanova, “Exact Orders of Computational (Numerical) Diameters in Problems of Reconstructing Functions and Sampling Solutions of the Klein–Gordon Equation from Fourier Coefficients”, Proc. Steklov Inst. Math., 282, suppl. 1 (2013), S165–S191  mathnet  crossref  crossref  isi  elib
    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, “On best harmonic synthesis of periodic functions”, J. Math. Sci., 209:1 (2015), 115–129  mathnet  crossref  mathscinet
    5. 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
    6. 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
    7. Osipenko K.Yu., “Optimal recovery of operators and multidimensional Carlson type inequalities”, J. Complex., 32:1 (2016), 53–73  crossref  mathscinet  zmath  isi  scopus
    8. Osipenko K.Yu., “Recovery of Derivatives For Functions Defined on the Semiaxis”, J. Complex., 48 (2018), 111–118  crossref  mathscinet  zmath  isi  scopus
    9. N. Temirgaliev, A. Zh. Zhubanysheva, “Kompyuternyi (vychislitelnyi) poperechnik v kontekste obschei teorii vosstanovleniya”, Izv. vuzov. Matem., 2019, no. 1, 89–97  mathnet  crossref
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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