M. K. Kerimov, E. V. Selimkhanov, “On exact estimates of the convergence rate of Fourier series for functions of one variable in the space <nobr>$L_2[-\pi,\pi]$</nobr>”, Zh. Vychisl. Mat. Mat. Fiz., 2016, Volume 56, Number 5,Pages <nobr>730

This article is cited 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. Kerimov^a, E. V. Selimkhanov^b

^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

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.

UDC: 519.651

Received: 21.12.2015

DOI: 10.7868/S0044466916050094