Approximation of ˉψintegrals−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 LˉψN in the uniform and integral metrics. The results obtained are extended to the case where the classes LˉψN are the classes of convolutions of functions from 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 LˉψN 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
Stepanets, O. I. “Approximation of ˉψintegrals−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