2019
Том 71
№ 10

# Approximation of $\bar {\psi} - integrals$−integrals of periodic functions by Fourier sums (small smoothness). Iof periodic functions by Fourier sums (small smoothness). I

Stepanets O. I.

Abstract

We investigate the rate of convergence of Fourier series on the classes $L^{\bar {\psi} } \text{N}$ in the uniform and integral metrics. The results obtained are extended to the case where the classes $L^{\bar {\psi} } \text{N}$ are the classes of convolutions of functions from $\text{N}$ with kernels with slowly decreasing coefficients. In particular, we obtain asymptotic equalities for the upper bounds of deviations of the Fourier sums on the sets $L^{\bar {\psi} } \text{N}$ which are solutions of the Kolmogorov-Nikol’skii problem. In addition, we establish an analog of the well-known Lebesgue inequality.

English version (Springer): Ukrainian Mathematical Journal 50 (1998), no. 2, pp 314–333.

Citation Example: Stepanets O. I. Approximation of $\bar {\psi} - integrals$−integrals of periodic functions by Fourier sums (small smoothness). Iof periodic functions by Fourier sums (small smoothness). I // Ukr. Mat. Zh. - 1998. - 50, № 2. - pp. 274-291.

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