Geodesic
Problems in the Approximation of $2\pi$-Periodic Functions by Fourier Sums in the Space $L_2(2\pi)$
Matematičeskie zametki, Tome 76 (2004) no. 6, pp. 803-811.

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In this paper, using the Steklov function, we introduce the modulus of continuity and define the classes of functions $W_{2,\varphi}^{r,k}$ and $W_\varphi^{r,k}$ in the spaces $L_2$ and $C$. For the class $W_{2,\varphi}^{r,k}$, we calculate the order of the Kolmogorov width and, for the class $W_\varphi^{r,k}$, we obtain an estimate of the error of a quadrature formula. 
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     title = {Problems in the {Approximation} of $2\pi${-Periodic} {Functions} by {Fourier} {Sums} in the {Space} $L_2(2\pi)$},
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V. A. Abilov; F. V. Abilova. Problems in the Approximation of $2\pi$-Periodic Functions by Fourier Sums in the Space $L_2(2\pi)$. Matematičeskie zametki, Tome 76 (2004) no. 6, pp. 803-811. http://geodesic.mathdoc.fr/item/MZM_2004_76_6_a0/

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