arXiv subjects

S. Ya. Yanchenko

Publications and source records attributed to S. Ya. Yanchenko.

8 recordsLinked to original sources

arXiv2024

Best approximations for classes of periodic functions of many variables with bounded dominating mixed derivative

We established exact in order estimates an approximation of the Sobolev classes $W^{\boldsymbol{r}}_{p,\boldsymbolα}(\mathbb{T}^d)$ 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 $B_{q,1}(\mathbb{T}^d)$, $1 \leqslant p, q < \infty$.

math.CA↗

arXiv2024

Approximation of functions of many variables from the generalization Nikol'skii-Besov type classes in the uniform and integral metrics

We obtain the exact order estimates of the approximation of the functions of many variables from the generalized Nikol'skii-Besov classes $B^Ω_{p,θ}(\mathbb{R}^d)$ 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 $Ω$ coincide with the well-known classical Nikol'skii-Besov isotropic classes.

math.CA↗

arXiv2021

Estimates for the entropy numbers of the Nikol'skii-Besov classes of periodic functions of many variables in the space of quasi-continuous functions

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

math.CA↗

arXiv2019

Approximation of Nikol'skii-Besov functional classes $S^r_{1,θ}B(\mathbb{R}^d)$ by entire functions of a special form

We establish the exact-order estimates for the approximation of functions from the Nikol'skii-Besov classes $S^{\boldsymbol{r}}_{1,θ} B(\mathbb{R}^d)$, $d\geqslant 1$, 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 $L_{\infty}(\mathbb{R}^d)$.

math.CA↗

arXiv2018

Approximative characteristics of classes of functions $S^Ω_{p,θ}B(\mathbb{R}^d)$ with a given majorant of mixed modulus of smoothness

We obtain order estimates of approximation of functions from the classes $S^Ω_{p,θ}B (\mathbb{R}^d)$ in the space $L_q(\mathbb{R}^d)$, $1<p<q<\infty$, by entire functions of exponential type with supports of their Fourier transforms in sets generated by the level surfaces of a function $Ω$.

math.CA↗

arXiv2017

Order estimates of approximation characteristics of functions from anisotropic Nikol'skii-Besov classes

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

math.CA↗

arXiv2017

The best approximation of functions from anisotropic Nikol'skii-Besov classes defined in $\mathbb{R}^d$

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.

math.CA↗

arXiv2016

Order estimates of approximative characteristics of functions from classes $S^{r}_{1,θ}B(\mathbb{R}^d)$

We obtained exact order estimates of approximation of the classes $S^{\boldsymbol{r}}_{1,θ}B$ 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, $L_q(\mathbb{R}^d)$, $1<q\leqslant \infty$.

math.CA↗