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Mat. Sb., 2002, Volume 193, Number 3, Pages 79–100 (Mi msb637)  

This article is cited in 36 scientific papers (total in 36 papers)

Optimal recovery of functions and their derivatives from Fourier coefficients prescribed with an error

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 functions and their derivatives from approximate values of their Fourier coefficients are considered. Explicit expressions for optimal recovery methods in classes of smooth and analytic functions defined on various compact manifolds are presented.


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English version:
Sbornik: Mathematics, 2002, 193:3, 387–407

Bibliographic databases:

UDC: 517.5
MSC: Primary 41A65; Secondary 90C25, 46E20
Received: 01.11.2001

Citation: G. G. Magaril-Il'yaev, K. Yu. Osipenko, “Optimal recovery of functions and their derivatives from Fourier coefficients prescribed with an error”, Mat. Sb., 193:3 (2002), 79–100; Sb. Math., 193:3 (2002), 387–407

Citation in format AMSBIB
\by G.~G.~Magaril-Il'yaev, K.~Yu.~Osipenko
\paper Optimal recovery of functions and their derivatives from Fourier coefficients
prescribed with an~error
\jour Mat. Sb.
\yr 2002
\vol 193
\issue 3
\pages 79--100
\jour Sb. Math.
\yr 2002
\vol 193
\issue 3
\pages 387--407

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    2. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “Optimal Recovery of Functions and Their Derivatives from Inaccurate Information about the Spectrum and Inequalities for Derivatives”, Funct. Anal. Appl., 37:3 (2003), 203–214  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. G. G. Magaril-Il'yaev, K. Yu. Osipenko, V. M. Tikhomirov, “Indefinite Knowledge about an Object and Accuracy of Its Recovery Methods”, Problems Inform. Transmission, 39:1 (2003), 104–118  mathnet  crossref  mathscinet  zmath
    4. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “Optimal recovery of values of functions and their derivatives from inaccurate data on the Fourier transform”, Sb. Math., 195:10 (2004), 1461–1476  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. K. Yu. Osipenko, “O vosstanovlenii resheniya zadachi Dirikhle po netochnym iskhodnym dannym”, Vladikavk. matem. zhurn., 6:4 (2004), 55–62  mathnet  mathscinet  zmath  elib
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    7. E. V. Vvedenskaya, “Ob optimalnom vosstanovlenii resheniya uravneniya teploprovodnosti po netochno zadannoi temperature v razlichnye momenty vremeni”, Vladikavk. matem. zhurn., 8:1 (2006), 16–21  mathnet  mathscinet  elib
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    10. E. A. Balova, “Optimal Reconstruction of the Solution of the Dirichlet Problem from Inaccurate Input Data”, Math. Notes, 82:3 (2007), 285–294  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    11. R. R. Akopian, “Optimal recovery of functions analytical in a half-plane”, Proc. Steklov Inst. Math. (Suppl.), 259, suppl. 2 (2007), S1–S11  mathnet  crossref  elib
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    13. Maergoiz L., Tarkhanov N., “Optimal recovery from a finite set in Banach spaces of entire functions”, Adv. Math., 222:5 (2009), 1727–1745  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    14. Chudova S.S., “Optimalnoe vosstanovlenie raznostei posledovatelnostei po netochnoi informatsii”, Vestn. Rossiiskogo un-ta druzhby narodov. Ser.: Matem., inform., fiz., 2009, no. 3, 12–15  elib
    15. Vvedenskaya E.V., “On the optimal recovery of a solution of a system of linear homogeneous differential equations”, Differ. Equ., 45:2 (2009), 262–266  crossref  mathscinet  zmath  isi  elib  elib  scopus
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    19. A. V. Arutyunov, S. E. Zhukovskiy, Z. T. Mingaleeva, “Differential properties of the minimum function for diagonalizable quadratic problems”, Comput. Math. Math. Phys., 52:10 (2012), 1342–1350  mathnet  crossref  mathscinet  zmath
    20. E. O. Sivkova, “Ob optimalnom vosstanovlenii laplasiana funktsii po ee netochno zadannomu preobrazovaniyu Fure”, Vladikavk. matem. zhurn., 14:4 (2012), 63–72  mathnet
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    23. 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
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    27. A. Zh. Zhubanysheva, N. Temirgaliev, “Informative cardinality of trigonometric Fourier coefficients and their limiting error in the discretization of a differentiation operator in multidimensional Sobolev classes”, Comput. Math. Math. Phys., 55:9 (2015), 1432–1443  mathnet  crossref  crossref  mathscinet  isi  elib  elib
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    30. Balgimbayeva Sh., “Recovery of partial differential operators on classes of periodic functions with mixed smoothness”, INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2016) (Almaty, Kazakhstan, 7–10 September 2016), AIP Conference Proceedings, 1759, eds. Ashyralyev A., Lukashov A., Amer Inst Physics, 2016, 020091  crossref  isi  scopus
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    32. Bagramyan T., “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
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