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

DOI10.1070/SM2004v195n10ABEH000853zbMath1072.42002OpenAlexW2037774877MaRDI QIDQ5693783

Konstantin Yu. Osipenko, Gregorij G. Magaril-Il'yaev

Publication date: 28 September 2005

Published in: Sbornik: Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/sm2004v195n10abeh000853

zbMATH Keywords

Fourier transformoptimal recoverySteckin problem

Mathematics Subject Classification ID

Trigonometric approximation (42A10) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16)

Related Items (10)

On best harmonic synthesis of periodic functions ⋮ Best recovery of the Laplace operator of a function and sharp inequalities ⋮ The best approximation of a set whose elements are known approximately ⋮ Optimal recovery in weighted spaces with homogeneous weights ⋮ Optimal recovery of operators and multidimensional Carlson type inequalities ⋮ Predual spaces for the space of \((p, q)\)-multipliers and their application in Stechkin's problem on approximation of differentiation operators ⋮ Exact orders of computational (numerical) diameters in problems of reconstructing functions and sampling solutions of the Klein-Gordon equation from Fourier coefficients ⋮ Recovery of derivatives for functions defined on the semiaxis ⋮ Computational (numerical) diameter in a context of general theory of a recovery ⋮ Inequalities for derivatives with the Fourier transform

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