Abstract
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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Abilov, V.A., Abilova, F.V. Problems in the Approximation of \(2\pi \)-Periodic Functions by Fourier Sums in the Space \(L_2 (2\pi )\) . Mathematical Notes 76, 749–757 (2004). https://doi.org/10.1023/B:MATN.0000049674.45111.71
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DOI: https://doi.org/10.1023/B:MATN.0000049674.45111.71