2019
Том 71
№ 11

All Issues

Yanchenko S. Ya.

Articles: 6
Article (Ukrainian)

Approximative characteristics of the Nikol’skii – Besov classes of functions $S_{1, θ}^r B(\mathbb{R}^d)$

Radchenko O. Ya., Yanchenko S. Ya.

↓ Abstract

Ukr. Mat. Zh. - 2019. - 71, № 10. - pp. 1405-1421

UDC 517.51
We establish the exact-order estimates for the approximation of the classes $S^{\boldsymbol{r}}_{1,\theta}B \left(\mathbb{R}^d\right)$ by entire functions of exponential type with supports of their Fourier transforms lying in a step hyperbolic cross. The error of approximation is estimated in the metric of the Lebesgue space $L_q\left(\mathbb{R}^d\right),\; 1 < q \leq \infty.$

Article (Ukrainian)

Best approximation of the functions from anisotropic Nikol’skii – Besov classes defined in $R^d$

Yanchenko S. Ya.

↓ Abstract

Ukr. Mat. Zh. - 2018. - 70, № 4. - pp. 574-582

We establish the exact-order estimates for the best approximations of the functions from anisotropic Nikol’skii – Besov classes of functions of several variables by entire functions in the Lebesgue spaces.

Article (Ukrainian)

Order estimates for the approximative characteristics of functions from the classes $S_{p,θ}^{Ω} B(R^d)$ with a given majorant of generalized mixed modules of smoothness in the uniform metric

Yanchenko S. Ya.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2016. - 68, № 12. - pp. 1705-1714

We establish the exact-order estimates of approximation for the classes $S_{p,θ}^{Ω} B$ of functions of several variables defined on $R^d$ in the norm of $L_{\infty} (R^d)$ by entire functions of exponential type with supports of their Fourier transforms in the sets generated by the level surfaces of a function $\Omega$.

Article (Ukrainian)

Approximation of Functions from the Isotropic Nikol’skii–Besov Classes in the Uniform and Integral Metrics

Yanchenko S. Ya.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2015. - 67, № 10. - pp. 1423-1433

We obtain the exact-order estimations for the approximation of the isotropic Nikol’skii–Besov classes of functions of several variables by the de la Vallée-Poussin-type sums in metrics of the spaces $L_{∞}(ℝ^d)$ and $L_1(ℝ^d)$.

Article (Ukrainian)

Approximation of the classes $S^r_{p,θ}B(\mathbb{R}^d)$ of functions of many variables by entire functions of a special form

Yanchenko S. Ya.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2010. - 62, № 8. - pp. 1124–1138

Exact-order estimates are obtained for the approximations of the functional classes $S^r_{p,θ}B(\mathbb{R}^d)$ by entire functions of a special form.

Article (Ukrainian)

Approximations of classes $B^{Ω}_{p,θ}$ of functions of many variables by entire functions in the space $L_q (R^d)$

Yanchenko S. Ya.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2010. - 62, № 1. - pp. 123–135

Exact-order estimates are obtained for the best approximations of the classes $B^{Ω}_{p,θ}$ of functions of many variables by entire functions of the exponential type in the space $L_q (R^d)$.