2018
Том 70
№ 12

# Rukasov V. I.

Articles: 19
Article (Ukrainian)

### Approximation by de la Vallée-Poussin operators on the classes of functions locally summable on the real axis

Ukr. Mat. Zh. - 2010. - 62, № 7. - pp. 968–978

For the least upper bounds of deviations of the de la Vallée-Poussin operators on the classes $\widehat{L}^{\psi}_{\beta}$ of rapidly vanishing functions $ψ$ in the metric of the spaces $\widehat{L}_p,\; 1 ≤ p ≤ ∞$, we establish upper estimates that are exact on some subsets of functions from $\widehat{L}_p$.

Obituaries (Ukrainian)

### Alexander Ivanovich Stepanets

Ukr. Mat. Zh. - 2007. - 59, № 12. - pp. 1722-1724

Brief Communications (Russian)

### Approximation of Classes of ψ-Integrals of Periodic Functions of Many Variables by Rectangular Linear Means of Their Fourier Series

Ukr. Mat. Zh. - 2005. - 57, № 4. - pp. 564–570

We obtain asymptotic equalities for deviations of rectangular linear means of Fourier series on classes of ψ-integrals of multivariable functions

Article (Russian)

### Approximation of Continuous Functions of Low Smoothness by de la Vallee-Poussin Operators

Ukr. Mat. Zh. - 2005. - 57, № 3. - pp. 394–399

We study some problems of the approximation of continuous functions defined on the real axis. As approximating aggregates, the de la Vallee-Poussin operators are used. We establish asymptotic equalities for upper bounds of the deviations of the de la Vallee-Poussin operators from functions of low smoothness belonging to the classes $\hat C^{\bar \psi } \mathfrak{N}$.

Article (Russian)

### Approximation of Continuous Functions by de La Vallee-Poussin Operators

Ukr. Mat. Zh. - 2005. - 57, № 2. - pp. 230–238

For $\sigma \rightarrow \infty$, we study the asymptotic behavior of upper bounds of deviations of functions blonding to the classes $\widehat{C}_{\infty}^{\overline{\Psi}}$ and $\widehat{C}^{\overline{\Psi}} H_{\omega}$ from the so-called Vallee Poussin operators. We find asymptotic equalities that, in some important cases, guarantee the solution of the Kolmogorov - Nikol's'kyi problem for the Vallee Poussin operators on the classes $\widehat{C}_{\infty}^{\overline{\Psi}}$ and $\widehat{C}^{\overline{\Psi}} H_{\omega}$.

Article (Russian)

### Approximation of Classes of Analytic Functions by de la Vallée-Poussin Sums

Ukr. Mat. Zh. - 2003. - 55, № 6. - pp. 806-816

For upper bounds of the deviations of de la Vallée-Poussin sums taken over classes of functions that admit analytic extensions to a fixed strip of the complex plane, we obtain asymptotic equalities. In certain cases, these equalities give a solution of the corresponding Kolmogorov–Nikol'skii problem.

Article (Russian)

### Best “Continuous” $n$-Term Approximations in the Spaces $S_\phi ^p$

Ukr. Mat. Zh. - 2003. - 55, № 5. - pp. 663-670

We find exact values of upper bounds for the best approximations of $q$-ellipsoids by polynomials of degree $n$ in the spaces $S_\phi ^p$ in the case where the approximating polynomials are constructed on the basis of $n$-dimensional subsystems chosen successively from a given orthonormal system ϕ.

Article (Russian)

### Best n-Term Approximations in Spaces with Nonsymmetric Metric

Ukr. Mat. Zh. - 2003. - 55, № 4. - pp. 500-509

We determine exact values of n-term approximations of q-ellipsoids in the spaces $S_\phi^{p, \mu}$ .

Article (Russian)

### Approximation of Continuous Functions by de la Vallée-Poussin Operators

Ukr. Mat. Zh. - 2003. - 55, № 3. - pp. 414-424

For the upper bounds of the deviations of a function defined on the entire real line from the corresponding values of the de la Vallée-Poussin operators, we find asymptotic equalities that give a solution of the well-known Kolmogorov–Nikol'skii problem.

Article (Russian)

### Spaces $S^p$ with Nonsymmetric Metric

Ukr. Mat. Zh. - 2003. - 55, № 2. - pp. 264-277

We determine exact values of the best approximations and Kolmogorov widths of $q$-ellipsoids in spaces $S_\phi ^{p,{\mu}}$ defined by anisotropic metric.

Article (Ukrainian)

### Approximation of Analytic Periodic Functions by de la Vallée-Poussin Sums

Ukr. Mat. Zh. - 2002. - 54, № 12. - pp. 1653-1669

We investigate the approximation properties of the de la Vallée-Poussin sums on the classes $C_{\beta }^q H_{\omega }$ . We obtain asymptotic equalities that, in certain cases, guarantee the solvability of the Kolmogorov–Nikol'skii problem for the de la Vallée-Poussin sums on the classes $C_{\beta }^q H_{\omega }$ .

Article (Russian)

### Approximation Properties of the de la Vallée-Poussin Method

Ukr. Mat. Zh. - 2002. - 54, № 8. - pp. 1100-1125

We present a survey of results concerning the approximation of classes of periodic functions by the de la Vallée-Poussin sums obtained by various authors in the 20th century.

Anniversaries (Ukrainian)

### Oleksandr Ivanovych Stepanets' (on his 60-th birthday)

Ukr. Mat. Zh. - 2002. - 54, № 5. - pp. 579-580

Article (Russian)

### Approximation of the Classes $C^{{\bar \psi }} H_{\omega }$ by de la Vallée-Poussin Sums

Ukr. Mat. Zh. - 2002. - 54, № 5. - pp. 681-691

We investigate the problem of the approximation of the classes $C^{{\bar \psi }} H_{\omega }$ introduced by Stepanets in 1996 by the de la Valée-Poussin sums. We obtain asymptotic equalities that give a solution of the Kolmogorov–Nikol'skii problem for the de la Valée-Poussin sums on the classes Cψ¯HωCψ¯Hω in several important cases.

Article (Russian)

### Approximation of $\overline \psi$-Integrals of Periodic Functions by de la Vallée-Poussin Sums (Low Smoothness)

Ukr. Mat. Zh. - 2001. - 53, № 12. - pp. 1641-1653

We investigate the asymptotic behavior of the upper bounds of deviations of linear means of Fourier series from the classes $C_{\infty} ^{\psi}$. In particular, we obtain asymptotic equalities that give a solution of the Kolmogorov – Nikol'skii problem for the de la Vallée-Poussin sums on the classes $C_{\infty} ^{\psi}$.

Brief Communications (Russian)

### Approximation of the classes $C_{β}^{ψ} H_{ω}$ by generalized de la Valiée-Poussin sums

Ukr. Mat. Zh. - 1997. - 49, № 4. - pp. 606-610

On the classes of periodic functions $C_{β}^{ψ} H_{ω}$, we study approximating properties of trigonometric polynomials generated by methods for summation of Fourier series.

Article (Ukrainian)

### Approximations of functions of class C ψ β ∞ by linear means of their fourier series

Ukr. Mat. Zh. - 1987. - 39, № 4. - pp. 478–483

Article (Ukrainian)

### Approximation by triangular fourier sums on classes of continuous periodic functions of two variables

Ukr. Mat. Zh. - 1983. - 35, № 2. - pp. 249—254

Article (Ukrainian)

### Estimates of errors in interpolating trigonometric polynomials with equidistant nodes on classes of continuous periodic functions of several variables

Ukr. Mat. Zh. - 1983. - 35, № 1. - pp. 70—75