Myronyuk V. Approximative characteristics of the classes of functions of several variables

The thesis investigates some approximate characteristics of the classes B^{omega}_{p,theta} and B^{R}_{p,theta} of periodic functions of several variables as well as the classes B^{omega}_{p,theta}(R^d) and S^{Omega}_{p,theta}B(R^d) of the functions defined on R^d. It sets exact order estimates of the deviation of "cubic" Fourier sums of periodic functions from the classes B^{omega}_{p,theta} within the space L_p(pi_d) with pє{1,infty}. It obtains exact order estimates of trigonometric approximations and Kolmogorov widths of the classes B^{R}_{p,theta} within the space L_q(pi_d) by some correlations of parameters p and q. The thesis finds exact order estimates of the approximation of the classes B^{omega}_{p,theta}(R^d) by the entire functions of exponential type within the space L_q(R^d) by 1<p <= q < infty and p=1, 1<q<infty. Besides it studies the behaviour of the approximation of the classes S^{Omega}_{p,theta}B(R^d) by entire functions with the carrier of Fourier transformation of special type in the space L_q(R^d) by 1<p<q < infty and 1<p=q <= 2.