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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2016, Volume 56, Number 5, Pages 730–741
DOI: https://doi.org/10.7868/S0044466916050094 (Mi zvmmf10394) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On exact estimates of the convergence rate of Fourier series for functions of one variable in the space $L_2[-\pi,\pi]$

M. K. Kerimova, E. V. Selimkhanovb

a Dorodnicyn Computer Center, Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia
b Dagestan State University, ul. Gadzhieva 43a, Makhachkala, 367025, Russia
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DOI: https://doi.org/10.7868/S0044466916050094
Abstract: The work is devoted to exact estimates of the convergence rate of Fourier series in the trigonometric system in the space of square summable $2\pi$-periodic functions with the Euclidean norm on certain classes of functions characterized by the generalized modulus of continuity. Some $N$-widths of these classes are calculated, and the residual term of one quadrature formula over equally spaced nodes for a definite integral connected with the issues under consideration is found.
Key words: Fourier series for functions of one variable, best approximation of functions, generalized modulus of continuity, widths of classes of functions, quadrature formula over equally spaced nodes for a definite integral, exact estimates of the convergence rate of Fourier series.
Received: 21.12.2015
English version:
Computational Mathematics and Mathematical Physics, 2016, Volume 56, Issue 5, Pages 717–729
DOI: https://doi.org/10.1134/S0965542516050092
Bibliographic databases:
Document Type: Article
UDC: 519.651
Language: Russian
Citation: M. K. Kerimov, E. V. Selimkhanov, “On exact estimates of the convergence rate of Fourier series for functions of one variable in the space $L_2[-\pi,\pi]$”, Zh. Vychisl. Mat. Mat. Fiz., 56:5 (2016), 730–741; Comput. Math. Math. Phys., 56:5 (2016), 717–729
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
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