Approximation of infinitely differentiable periodic functions by interpolation trigonometric polynomials

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