2018
Том 70
№ 9

All Issues

Stasyuk S. A.

Articles: 13
Article (Ukrainian)

Best $m$-term trigonometric approximation for periodic functions with low mixed smoothness from the Nikol’skii – Besov-type classes

Stasyuk S. A.

↓ Abstract

Ukr. Mat. Zh. - 2016. - 68, № 7. - pp. 983-1003

We establish the exact-order estimates of the best $m$-term trigonometric approximation for periodic multivariable functions (with low mixed smoothness) from the Nikol’skii – Besov-type classes.

Brief Communications (Ukrainian)

Kolmogorov Widths for Analogs of the Nikol’skii–Besov Classes with Logarithmic Smoothness

Stasyuk S. A.

↓ Abstract

Ukr. Mat. Zh. - 2015. - 67, № 11. - pp. 1579-1584

We establish the exact-order estimates of Kolmogorov widths and entropy numbers for analogs of the Nikol’skii–Besov classes with logarithmic smoothness.

Article (Russian)

Approximating Characteristics of the Analogs of Besov Classes with Logarithmic Smoothness

Stasyuk S. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2014. - 66, № 4. - pp. 493–499

We obtain the exact-order estimates of some approximating characteristics for the analogs of Besov classes of periodic functions of several variables (with logarithmic smoothness).

Brief Communications (Russian)

Best approximation of periodic functions of several variables from the classes $MB^{\omega}_{p,\theta}$

Stasyuk S. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 1. - pp. 140-144

We obtain exact-order estimates for the best approximation of periodic functions of several variables from the classes $MB^{\omega}_{p,\theta}$ by trigonometric polynomials with the "numbers" of harmonics from graded hyperbolic crosses in the metric of the space $L_q$.

Article (Russian)

Best $m$-term approximation of the classes $B ^{r}_{\infty, \theta}$ of functions of many variables by polynomials in the haar system

Stasyuk S. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 4. - pp. 549-555

We obtain the exact-order estimate for the best $m$-term approximation of the classes $B ^{r}_{\infty, \theta}$ of periodic functions of many variables by polynomials with respect to the Haar system in the metric of the space $L_q,\quad 1 < q < \infty$.

Article (Russian)

Best $m$-term trigonometric approximation for the classes $B^r_{p,θ}$ of functions of low smoothness

Stasyuk S. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2010. - 62, № 1. - pp. 104–111

We obtain an exact-order estimate for the best $m$-term trigonometric approximation of the Besov classes $B^r_{p,θ}$ of periodic functions of many variables of low smoothness in the space $L_q, \; 1 < p ≤ 2 < q < ∞$.

Article (Ukrainian)

Best M-term trigonometric approximations of the classes of periodic functions of many variables in the space Lq

Konohrai A. F., Stasyuk S. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 9. - pp. 1196 – 1214

We obtain order estimates for the best M-term trigonometric approximations of classes B Ωp,θ of periodic multivariable functions in the space Lq for some values of the parameters p and q.

Article (Ukrainian)

Best M-term orthogonal trigonometric approximations of the classes B Ωp,θ of periodic functions of many variables

Stasyuk S. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 5. - pp. 647 – 656

Order estimates of the best M-term orthogonal trigonometric approximations of the classes B Ωp,θ of multivariable functions in the metric of the space Lq are obtained for the case 1 < q < p < ∞.

Article (Ukrainian)

Approximation characteristics of the classes $B_{p,θ}^{Ω}$ of periodic functions of many variables

Fedunyk O. V., Stasyuk S. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 5. - pp. 692–704

We obtain exact order estimates for the approximation of the classes $B_{p,θ}^{Ω}$ of periodic functions of many variables in the space $L_q$ by using operators of orthogonal projection and linear operators satisfying certain conditions.

Article (Ukrainian)

Best Approximations and Kolmogorov and Trigonometric Widths of the Classes $B_{p,θ}^{Ω}$ of Periodic Functions of Many Variables

Stasyuk S. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 11. - pp. 1557-1568

We obtain estimates exact in order for the best approximations and Kolmogorov and trigonometric widths of the classes $B_{p,θ}^{Ω}$ of periodic functions of many variables in the space $L^q$ for certain values of the parameters $p$ and $q$.

Article (Ukrainian)

Approximation of the Classes $B_{p,θ}^Ω$ of Periodic Functions of Many Variables in Uniform Metric

Stasyuk S. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2002. - 54, № 11. - pp. 1551-1559

We obtain order estimates for the best $М$-term trigonometric approximations and approximations by Fourier sums for the classes $B_{p,θ}^Ω$ of periodic functions of many variables in the uniform metric.

Article (Ukrainian)

Trigonometric Widths of the Classes $B_{p,θ}^{Ω}$ of Periodic Functions of Many Variables

Stasyuk S. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2002. - 54, № 5. - pp. 700-705

We obtain exact order estimates for the trigonometric widths of the classes BΩp,θBp,θΩ of periodic functions of many variables in the space $L_{q, 1}\; < p ≤ 2 ≤ q < p/(p − 1)$.

Article (Ukrainian)

Best $M$-Term Trigonometric Approximations of the Classes $B_{p,θ}^Ω$ of Functions of Many Variables

Stasyuk S. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2002. - 54, № 3. - pp. 381-394

We obtain exact order estimates for the best $M$-term trigonometric approximations of the classes $B_{p,θ}^Ω$ of functions of many variables in the space $L_{q, 1} < p < q < ∞, q > 2$.