Derevyanko N. The widths of the classes of periodic functions of several variables

Investigated in the thesis are the widths of the classes B_{p,theta}^omega and S_p^Omega H of periodic functions of several variables. Obtained here are the exact order estimates of linear, orthoprojective and trigonometric widths of the classes B_{p,theta}^omega in the space L_q(pi_d) for some relations between parameters p and q. The fact that in some cases the order estimates of these widths coincide with the order estimates of the Kolmogorov widths which were obtained before was revealed during the research. The exact order estimates of orthoprojective widths of the classes S_p^Omega H in the space L_p(pi_d) for p in {1,infty} are obtained. For to prove this result established here are the upper order estimates for approximation of functions of classes S_p^Omega H by some linear methods constructed by using operators of special form. In addition obtained here are the order estimates of linear widths of the classes S_p^Omega H in the space L_q(pi_d) for some relations between parameters p and q.