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

This article is cited in 33 scientific papers (total in 33 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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    This publication is cited in the following articles:
    1. 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
    2. 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
    3. 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
    4. K. Yu. Osipenko, “O vosstanovlenii resheniya zadachi Dirikhle po netochnym iskhodnym dannym”, Vladikavk. matem. zhurn., 6:4 (2004), 55–62  mathnet  mathscinet  zmath  elib
    5. K. Yu. Osipenko, “The Hardy–Littlewood–Pólya inequality for analytic functions in Hardy–Sobolev spaces”, Sb. Math., 197:3 (2006), 315–334  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. 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
    7. E. A. Balova, “Ob optimalnom vosstanovlenii resheniya zadachi Dirikhle v koltse”, Vladikavk. matem. zhurn., 8:2 (2006), 3–11  mathnet  mathscinet  elib
    8. N. D. Vysk, K. Yu. Osipenko, “Optimal Reconstruction of the Solution of the Wave Equation from Inaccurate Initial Data”, Math. Notes, 81:6 (2007), 723–733  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    9. 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
    10. 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
    11. Osipenko K.Yu., Wedenskaya E.V., “Optimal recovery of solutions of the generalized heat equation in the unit ball from inaccurate data”, J. Complexity, 23:4-6 (2007), 653–661  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    12. 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
    13. 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
    14. 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
    15. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “Optimal recovery of the solution of the heat equation from inaccurate data”, Sb. Math., 200:5 (2009), 665–682  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    16. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “On the reconstruction of convolution-type operators from inaccurate information”, Proc. Steklov Inst. Math., 269 (2010), 174–185  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    17. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “On Optimal Harmonic Synthesis from Inaccurate Spectral Data”, Funct. Anal. Appl., 44:3 (2010), 223–225  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    18. 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
    19. E. O. Sivkova, “Ob optimalnom vosstanovlenii laplasiana funktsii po ee netochno zadannomu preobrazovaniyu Fure”, Vladikavk. matem. zhurn., 14:4 (2012), 63–72  mathnet
    20. Arthur DeGraw, “Optimal Recovery of Holomorphic Functions from Inaccurate Information about Radial Integration”, AJCM, 02:04 (2012), 258  crossref  mathscinet
    21. G. G. Magaril-Il'yaev, E. O. Sivkova, “Best recovery of the Laplace operator of a function from incomplete spectral data”, Sb. Math., 203:4 (2012), 569–580  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    22. 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
    23. 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
    24. N. Temirgaliev, Sh. K. Abikenova, A. Zh. Zhubanysheva, G. E. Taugynbaeva, “Discretization of solutions to a wave equation, numerical differentiation, and function reconstruction for a computer (computing) diameter”, Russian Math. (Iz. VUZ), 57:8 (2013), 75–80  mathnet  crossref
    25. 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
    26. 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
    27. S. A. Unuchek, “Optimalnoe vosstanovlenie proizvodnoi funktsii po netochno zadannym proizvodnym drugikh poryadkov i samoi funktsii”, Vladikavk. matem. zhurn., 18:3 (2016), 60–71  mathnet
    28. Osipenko K.Yu., “Optimal recovery of operators and multidimensional Carlson type inequalities”, J. Complex., 32:1 (2016), 53–73  crossref  mathscinet  zmath  isi  scopus
    29. 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
    30. Babenko V., Babenko Yu., Parfinovych N., Skorokhodov D., “Optimal recovery of integral operators and its applications”, J. Complex., 35 (2016), 102–123  crossref  mathscinet  zmath  isi  scopus
    31. 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
    32. A. V. Arutyunov, K. Yu. Osipenko, “Recovering linear operators and Lagrange function minimality condition”, Siberian Math. J., 59:1 (2018), 11–21  mathnet  crossref  crossref  isi  elib
    33. D. B. Bazarkhanov, “Lineinoe vosstanovlenie psevdodifferentsialnykh operatorov na klassakh gladkikh funktsii na m-mernom tore. II”, Tr. IMM UrO RAN, 25, no. 4, 2019, 15–30  mathnet  crossref  elib
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