Stasyuk S. Approximation characteristics of classes of smooth functions of one and several variables

The thesis is devoted to the research of approximation characteristics of classes of periodic functions of one and several variables, more exactly, to obtaining of the order estimates of these characteristics for the NikolskiiBesov type classes of functions with wide range of smoothness. The exact order estimates of the best m-term trigonometric approximation of the Nikolskii–Besov classes of periodic multivariate functions with small isotropic smoothness are obtained. The exact order estimates of some approximation characteristics of the Nikolskii–Besov type classes of periodic functions with logarithmic smoothness are found. The exact order estimates of the best approximation of the Nikolskii-Besov classes of periodic multivariate functions with generalized mixed smoothness by trigonometric polynomials with harmonic “numbers” from step hyperbolic crosses are obtained. The exact order estimates of the best m-term trigonometric approximation of the Nikolskii–Besov type classes of periodic multivariate functions with wide range of smoothness are found. The exact order estimates of the best m-term approximation by the polynomials constructed by the tensor Haar system of the Nikolskii type classes of periodic multivariate functions with mixed generalized smoothness are obtained.