2017
Том 69
№ 6

# Approximation of infinitely differentiable periodic functions by interpolation trigonometric polynomials

Serdyuk A. S.

Abstract

We establish asymptotically unimprovable interpolation analogs of Lebesgue-type inequalities on the classes of periodic infinitely differentiable functions C Ψ β C whose elements can be represented in the form of convolutions with fixed generating kernels. We obtain asymptotic equalities for upper bounds of approximations by interpolation trigonometric polynomials on the classes C Ψ β,∞ and C Ψ β H ω.

English version (Springer): Ukrainian Mathematical Journal 56 (2004), no. 4, pp 601-613.

Citation Example: Serdyuk A. S. Approximation of infinitely differentiable periodic functions by interpolation trigonometric polynomials // Ukr. Mat. Zh. - 2004. - 56, № 4. - pp. 495–505.

Full text