Email this article On exact estimates of the convergence rate of fourier series for functions of one variable in the space L2[–π, π]
- Authors: Kerimov M.K.1, Selimkhanov E.V.2
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Affiliations:
- Dorodnicyn Computer Center, Federal Research Center “Computer Science and Control”
- Dagestan State University
- Issue: Vol 56, No 5 (2016)
- Pages: 717-729
- Section: Article
- URL: https://journals.rcsi.science/0965-5425/article/view/178425
- DOI: https://doi.org/10.1134/S0965542516050092
- ID: 178425
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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 2π-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.
About the authors
M. K. Kerimov
Dorodnicyn Computer Center, Federal Research Center “Computer Science and Control”
Author for correspondence.
Email: comp_math@ccas.ru
Russian Federation, ul. Vavilova 40, Moscow, 119333
E. V. Selimkhanov
Dagestan State University
Author for correspondence.
Email: SelimEm@yandex.ru
Russian Federation, ul. Gadzhieva 43a, Makhachkala, 367025
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