Solich K. Bilinear approximations of classes of periodic functions of many variables

The thesis cover the investigation of approximative characteristics of classes of periodical functions of many variables. The exact order estimates of bilinear approximations of periodic functions of 2d variables, generated by shift of the argument functions of d variables of classes B_{p,theta}^Omega and S_{p,theta}^Omega B are established. The behavior of the best bilinear approximations of periodic functions of several variables of class B_{p,theta}^Omega is investigated. We obtained the exact-order estimates of the Kolmogorov widths of these classes. The exact order estimates of the best bilinear approximations of periodical functions of two variables from the classes S_{p,theta}^Omega B are found.