Approximability of the classes of periodic functions of several variables by linear methods and best approximations

Abstract

Several questions of the approximability by linear methods of the Besov classes and of periodic functions of several variables, , are considered alongside their best approximations in the spaces and , respectively. Taken for approximation aggregates are trigonometric polynomials with spectrum in the step hyperbolic cross. Sharp (in order) estimates of the deviations of step hyperbolic Fourier sums on the classes , , in the space are also obtained.