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This article is cited in 32 scientific papers (total in 32 papers)
Problems in the Approximation of $2\pi$-Periodic Functions by Fourier Sums in the Space $L_2(2\pi)$
V. A. Abilov, F. V. Abilova
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.
Received: 12.02.2003
Citation:
V. A. Abilov, F. V. Abilova, “Problems in the Approximation of $2\pi$-Periodic Functions by Fourier Sums in the Space $L_2(2\pi)$”, Mat. Zametki, 76:6 (2004), 803–811; Math. Notes, 76:6 (2004), 749–757
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https://www.mathnet.ru/eng/mzm149https://doi.org/10.4213/mzm149 https://www.mathnet.ru/eng/mzm/v76/i6/p803
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Abstract page: | 775 | Full-text PDF : | 292 | References: | 58 | First page: | 1 |
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