Approximation of infinitely differentiable periodic functions by interpolation trigonometric polynomials - Serdyuk, A. S. (Ukrains’kyi Matematychnyi Zhurnal, 2004)
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.