Approximation of classes of analytic functions by de la Vallée Poussin sums in uniform metric - A. S. Serdyuk (Rendiconti di Matematica e delle Sue Applicazioni, 2012)
In this paper asymptotic equalities are found for the least upper bounds of deviations in the uniform metric of de la Vallée 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.