Geodesic
On exact estimates of the convergence rate of Fourier series for functions of one variable in the space $L_2[-\pi,\pi]$
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 5, pp. 730-741

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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. 
@article{ZVMMF_2016_56_5_a1,
     author = {M. K. Kerimov and E. V. Selimkhanov},
     title = {On exact estimates of the convergence rate of {Fourier} series for functions of one variable in the space $L_2[-\pi,\pi]$},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {730--741},
     publisher = {mathdoc},
     volume = {56},
     number = {5},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_5_a1/}
}
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M. K. Kerimov; E. V. Selimkhanov. On exact estimates of the convergence rate of Fourier series for functions of one variable in the space $L_2[-\pi,\pi]$. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 5, pp. 730-741. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_5_a1/