2018
Том 70
№ 2

Approximation of Classes of Analytic Functions by Fourier Sums in Uniform Metric

Serdyuk A. S.

Abstract

We find asymptotic equalities for upper bounds of approximations by Fourier partial sums in a uniform metric on classes of Poisson integrals of periodic functions belonging to unit balls of spaces $L_p,\quad 1 \leq p \leq \infty$. We generalize the results obtained to classes of $(\psi, \overline{\beta})$-differentiable functions (in the Stepanets sense) that admit analytical extension to a fixed strip of the complex plane.

English version (Springer): Ukrainian Mathematical Journal 57 (2005), no. 8, pp 1275-1296.

Citation Example: Serdyuk A. S. Approximation of Classes of Analytic Functions by Fourier Sums in Uniform Metric // Ukr. Mat. Zh. - 2005. - 57, № 8. - pp. 1079 – 1096.

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