2017
Том 69
№ 9

All Issues

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

Serdyuk A. S.

Full text (.pdf)


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.

Full text