This article is cited in 38 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.

UDC: 517.51.4

Received: 12.02.2003

DOI: 10.4213/mzm149

 English version: Mathematical Notes, 2004, 76:6, 749–757

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