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

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

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English version:
Sbornik: Mathematics, 2004, 195:10, 1461–1476

Bibliographic databases:

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

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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• http://mi.mathnet.ru/eng/msb853
• https://doi.org/10.4213/sm853
• http://mi.mathnet.ru/eng/msb/v195/i10/p67

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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
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
3. E. O. Sivkova, “Best recovery of the Laplace operator of a function and sharp inequalities”, J. Math. Sci., 209:1 (2015), 130–137
4. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “On best harmonic synthesis of periodic functions”, J. Math. Sci., 209:1 (2015), 115–129
5. K. Yu. Osipenko, “Optimal recovery of linear operators in non-Euclidean metrics”, Sb. Math., 205:10 (2014), 1442–1472
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
7. Osipenko K.Yu., “Optimal recovery of operators and multidimensional Carlson type inequalities”, J. Complex., 32:1 (2016), 53–73
8. Osipenko K.Yu., “Recovery of Derivatives For Functions Defined on the Semiaxis”, J. Complex., 48 (2018), 111–118
9. N. Temirgaliev, A. Zh. Zhubanysheva, “Computational (Numerical) diameter in a context of general theory of a recovery”, Russian Math. (Iz. VUZ), 63:1 (2019), 79–86
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