2018
Том 70
№ 9

# 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

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

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

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 $MB^{\omega}_{p,\theta}$

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

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

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

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

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

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

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

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

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

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 $L_{q, 1} < p < q < ∞, q > 2$.