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

  • O. I. Stepanets

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.
Published
25.02.1998
How to Cite
StepanetsO. I. “Approximation of $\bar {\psi} - integrals$−integrals of Periodic Functions by Fourier Sums (small smoothness). Iof Periodic Functions by Fourier Sums (small smoothness). I”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 50, no. 2, Feb. 1998, pp. 274-91, https://umj.imath.kiev.ua/index.php/umj/article/view/4961.
Section
Research articles