Corpus ID: 55275563

# Approximation of classes of analytic functions by de la Vallee Poussin sums in uniform metric

@article{Serdyuk2011ApproximationOC,
title={Approximation of classes of analytic functions by de la Vallee Poussin sums in uniform metric},
author={A. Serdyuk and Ie. Yu. Ovsii and A. Musienko},
journal={arXiv: Classical Analysis and ODEs},
year={2011}
}
• Published 2011
• Mathematics
• arXiv: Classical Analysis and ODEs
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.
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