Approximation of classes of analytic functions by de la Vallee Poussin sums in uniform metric
Classical Analysis and ODEs
2012-08-31 v1
Abstract
In this paper asymptotic equalities are found for the least upper bounds of deviations in the uniform metric of de la Vallee Poussin sums on classes of 2\pi-periodic (\psi,\beta)-differentiable functions admitting an analytic continuation into the given strip of the complex plane. As a consequence, asymptotic equalities are obtained on classes of convolutions of periodic functions generated by the Neumann kernel and the polyharmonic Poisson kernel.
Keywords
Cite
@article{arxiv.1112.0967,
title = {Approximation of classes of analytic functions by de la Vallee Poussin sums in uniform metric},
author = {A. S. Serdyuk and Ie. Yu. Ovsii and A. P. Musienko},
journal= {arXiv preprint arXiv:1112.0967},
year = {2012}
}
Comments
Supported in part by the Ukrainian Foundation for Basic Research (project no. 035/001)