Approximative characteristics and properties of operators of the best approximation of classes of functions from the Sobolev and Nikol'skii-Besov spaces

摘要

We have obtained the exact-order estimates for some approximative characteristics of the Sobolev classes W_(p,a)~γ and Nikol'skii-Besov classes B_(p,θ)~γ of periodic functions of one and several variables in the norm of the space B_(∞,1) • Properties of the linear operators realizing the orders of the best approximation for the classes B_(∞,θ)~γ in this space by trigonometric polynomials generated by a set of harmonics with "numbers" from step hyperbolic crosses are investigated.