Yanchenko S. The investigation of approximative characteristics of functions' classes of many variables

The investigation of approximative characteristics of classes $S^{r}_{p,theta}B$ and their generalizations $S^{Omega}_{p,theta}B$, and also classes $B^{r}_{p,theta}$ of functions which are defined at $mathbb{R}^d$ are studied in the thesis. Sharp in order estimates of the best approximation for functions with classes $S^{Omega}_{p,theta}B$ and $B^{r}_{p,theta}$ in the space $L_q(mathbb{R}^d)$, $1<q<infty$ by entire function of exponential type with supports of their Fourier transforms lying in step hyperbolic cross and cubic area respectively are obtained. The order estimates of approximation of functions of classes $S^r_{p,theta}B$ by entire functions, with supports of their Fourier transforms which focuses on the set, of a special form are also established. The sequential estimation of $e_m^{mathfrak{F}}(S^r_{p,theta}B)_q$ and $mathcal{E}^{gamma}_{Q_n}(S^r_{p,theta}B)_q$ in some cases are the same in order, but there is the ratio between the parameters under which the data approximate characteristics have differ order are revealed during the investigation.