2019
Том 71
№ 4

All Issues

Myronyuk V. V.

Articles: 5
Article (Ukrainian)

Widths of the anisotropic Besov classes of periodic functions of several variables

Myronyuk V. V.

↓ Abstract

Ukr. Mat. Zh. - 2016. - 68, № 8. - pp. 1080-1091

We establish the exact-order estimates of Kolmogorov and orthoprojective widths of anisotropic Besov classes of periodic functions of several variables in the spaces $L_q$.

Article (Ukrainian)

Kolmogorov widths of the anisotropic Besov classes of periodic functions of many variables

Myronyuk V. V.

↓ Abstract

Ukr. Mat. Zh. - 2016. - 68, № 5. - pp. 634-643

We establish exact-order estimates for the Kolmogorov widths of the anisotropic Besov classes of periodic functions of many variables in the spaces $L_q,\; 1 \leq q \leq \infty$.

Article (Ukrainian)

Trigonometric Approximations and Kolmogorov Widths of Anisotropic Besov Classes of Periodic Functions of Several Variables

Myronyuk V. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2014. - 66, № 8. - pp. 1117–1132

We describe the Besov anisotropic spaces of periodic functions of several variables in terms of the decomposition representation and establish the exact-order estimates of the Kolmogorov widths and trigonometric approximations of functions from unit balls of these spaces in the spaces L q .

Article (Ukrainian)

Approximation of Functions of Many Variables from the Classes $B_{p,θ}^{Ω} (ℝ^d)$ By Entire Functions of Exponential Type

Myronyuk V. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2014. - 66, № 2. - pp. 244–258

We obtain the decomposition representation of the norm of functions of many variables from the spaces $B_{p,θ}^{Ω} (ℝ^d)$ and establish the exact order estimates for the approximations of functions from the unit balls of these spaces by entire functions of exponential type in the space $L_q (ℝ^d)$.

Article (Ukrainian)

Approximation of the classes $B^{\Omega}_{p, \theta}$ of periodic functions of many variables by Fourier sums in the space $L_p$ with $p = 1, \infty$

Myronyuk V. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 9. - pp. 1204-1213

We obtain an exact-order estimate for the deviation of Fourier sums of periodic functions of many variables from the classes $B^{\Omega}_{p, \theta}$ in the space $L_p$ for $p = 1, \infty$.