2018
Том 70
№ 9

All Issues

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

Chaichenko S. O., Rukasov V. I.

↓ Abstract   |   Full text (.pdf)

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

Gorbachuk M. L., Lukovsky I. O., Mitropolskiy Yu. A., Romanyuk A. S., Rukasov V. I., Samoilenko A. M., Serdyuk A. S., Shevchuk I. A., Zaderei P. V.

Full text (.pdf)

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

Bodraya V. I., Novikov O. A., Rukasov V. I.

↓ Abstract   |   Full text (.pdf)

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

Rukasov V. I., Silin E. S.

↓ Abstract   |   Full text (.pdf)

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

Rukasov V. I., Silin E. S.

↓ Abstract   |   Full text (.pdf)

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

Rukasov V. I.

↓ Abstract   |   Full text (.pdf)

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 $S_\phi ^p$

Rukasov V. I., Stepanets O. I.

↓ Abstract   |   Full text (.pdf)

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

Rukasov V. I.

↓ Abstract   |   Full text (.pdf)

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

Rukasov V. I.

↓ Abstract   |   Full text (.pdf)

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

Rukasov V. I., Stepanets O. I.

↓ Abstract   |   Full text (.pdf)

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

Chaichenko S. O., Rukasov V. I.

↓ Abstract   |   Full text (.pdf)

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

Rukasov V. I., Stepanets O. I.

↓ Abstract   |   Full text (.pdf)

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)

Lukovsky I. O., Makarov V. L., Mitropolskiy Yu. A., Romanyuk A. S., Romanyuk V. S., Rukasov V. I., Samoilenko A. M., Serdyuk A. S., Shevchuk I. A., Zaderei P. V.

Full text (.pdf)

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

Chaichenko S. O., Rukasov V. I.

↓ Abstract   |   Full text (.pdf)

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)

Chaichenko S. O., Rukasov V. I.

↓ Abstract   |   Full text (.pdf)

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

Novikov O. A., Rukasov V. I.

↓ Abstract   |   Full text (.pdf)

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

Rukasov V. I.

Full text (.pdf)

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

Rukasov V. I., Stepanets O. I.

Full text (.pdf)

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

Rukasov V. I.

Full text (.pdf)

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