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

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

2011-12-05

arxiv.org/abs/1112.0967v1

Mathematics

Classical Analysis and ODEs

Supported in part by the Ukrainian Foundation for Basic Research (project no. 035/001)

Scientific paper

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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