Approximation of infinitely differentiable periodic functions by interpolation trigonometric polynomials

We establish asymptotically unimprovable interpolation analogs of Lebesgue-type inequalities on the classes of periodic infinitely differentiable functions CΨβC 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 CΨβ,∞ and CΨβHω.