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We established exact in order estimates an approximation of the Sobolev classes $W^{\boldsymbol{r}}_{p,\boldsymbol{\alpha}}(\mathbb{T}^d)$ of periodic functions of many variables with a bounded dominating mixed derivative. The approximation is made using trigonometric polynomials with the spectrum in step-hyperbolic crosses, and the error is estimated in the metric of the space $B_{q,1}(\mathbb{T}^d)$, $1 \leqslant p, q < \infty$., Comment: 18 pages, in Ukrainian

We obtain the exact order estimates of the approximation of the functions of many variables from the generalized Nikol'skii-Besov classes $B^{\Omega}_{p,\theta}(\mathbb{R}^d)$ by sums of de la Vallee Poussin type in the metrics space $L_{\infty}(\mathbb{R}^d)$ and $L_{1}(\mathbb{R}^d)$. These classes of functions for some given $\Omega$ coincide with the well-known classical Nikol'skii-Besov isotropic classes., Comment: 18 pages, in Ukrainian

We obtained exact-order estimates for the entropy numbers of the Nikol'skii-Besov classes $B^{\boldsymbol{r}}_{p,\theta}$ of periodic functions of many variables in the metric of the space of quasi-continuous functions., Comment: 15 pages, in Ukrainian

We establish the exact-order estimates for the approximation of functions from the Nikol'skii-Besov classes $S^{\boldsymbol{r}}_{1,\theta} B(\mathbb{R}^d)$, $d\geqslant 1$, by entire function exponential type with some restrictions for their spectrum. The error of the approximation is estimated in the metric of the Lebesgue space $L_{\infty}(\mathbb{R}^d)$., Comment: 11 pages, in Ukrainian

We obtained exact order estimates of the deviation of functions from anisotropic Nikol'skii-Besov classes $B^{\boldsymbol{r}}_{p,\theta}(\mathbb{R}^d)$ from their sections of the Fourier integral. The error of the approximation is estimated in the metric of Lebesgue space $L_{\infty}(\mathbb{R}^d)$., Comment: 9 pages, in Ukrainian

We establish the exact-order estimates of the best approximations of the functions from anisotropic Nikol'skii-Besov classes of several variables by entire functions in the Lebesgue spaces., Comment: 11 pages, in Ukrainian

We obtain order estimates of approximation of functions from the classes $S^{\Omega}_{p,\theta}B (\mathbb{R}^d)$ in the space $L_q(\mathbb{R}^d)$, $1

We obtained exact order estimates of approximation of the classes $S^{\boldsymbol{r}}_{1,\theta}B$ by entire functions of exponential type with supports of their Fourier transforms in step hyperbolic cross. The error of the approximation estimated in the metric of Lebesgue spaces, $L_q(\mathbb{R}^d)$, $1