Uniform Approximation of Periodical Functions by Trigonometric Sums of Special Type. (12th January 2014) - Serdyuk, A. S.; Ovsii, Ie. Yu.
Abstract : The approximation characteristics of trigonometric sums U n, p ψ of special type on the class C β, ∞ ψ of (ψ, β )-differentiable (in the sense of A. I. Stepanets) periodical functions are studied. Because of agreement between parameters of approximative sums and approximated classes, the solution of Kolmogorov-Nikol'skii problem is obtained in a sufficiently general case. It is shown that in a number of important cases these sums provide higher order of approximation in comparison with Fourier sums, de la Vallée Poussin sums, and others on the class C β, ∞ ψ in the uniform metric. The range of parameters in which the sums U n, p ψ give the order of the best uniform approximation on the classes C β, ∞ ψ is indicated.