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

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 2π-periodic (ψ,β)-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.

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

References in corpus (1)

• Uniform approximation of Poisson integrals of functions from the class H_omega by de la Vallee Poussin sums

Cited by in corpus (1)

• Lebesgue-type inequalities for de la Vallee Poussin sums on the sets of analytic and entire functions