Vol. 11 No. 3 (2014): Approximation Theory of Functions and Related Problems

UDC 517.5; 517.51; 517.53; 517.547.3; 517.983; 519.652

Collection of works of Institute of Mathematics of NAS of Ukraine.
Vol. 11, No. 3: Approximation Theory of Functions and Related Problems / Responsible Editor: A.S. Romanyuk. — Kyiv: Institute of Mathematics of NAS of Ukraine, 2014. — 344 p.

This issue contains a collection of papers contains articles, in which results on the theory of functions, functional analysis and related problems are presented. The book is intended for specialists in mathematical analysis, applied mathematics, PhD students and students of appropriate specialties.

Published: 2014-06-24

Research papers

Lower bounds for Kolmogorov widths in classes of convolutions with Neumann kernel

V. V. Bodenchuk

7-34
- PDF (Українська)
On the best approximation by “angles” in the mean on the plane $\mathbb{R}^2$ with the Chebyshev-Hermite weight.

S. B. Vakarchuk, A. V. Shvachko

35-46
- PDF (Русский)
Padé approximants of series connected with bilinear transformations

N. M. Gavrilyuk, A. P. Golub

47-55
- PDF (Українська)
On Lebesgue continuity on classes of $\bar{\psi}$-differentiable functions.

M. V. Gayevs’kyĭ

56-70
- PDF (Українська)
Two-dimensional Padé type approximants for some analytic functions of two variables

A. P. Golub, H. M. Veselovska

71-77
- PDF (Українська)
Construction of Padé approximants for Lauricella series by method of generalized moment representations

A. P. Golub, L. A. Chernetska

78-103
- PDF (Українська)
Solution of the Kolmogorov-Nikol’skii problem for three-harmonic Poisson integrals on classes $C^{\psi}_{\beta,\infty}$

U. Z. Grabova, I. V. Kal’chuk

104-127
- PDF (Українська)
Estimations of linear widths of the classes $H_p^\Omega$ periodic functions of many variables in the space $L_q$

N. V. Derev’yanko

128-145
- PDF (Українська)
Estimates of orthoprojection widths of classes $B^{\Omega}_{p,\theta}$ of periodic functions of several variables with given majorant of mixed moduli of continuity

A. F. Konograi, O. V. Fedunyk-Yaremchuk

146-165
- PDF (Українська)
Spectral analysis of two star graph with infinite chains

V. O. Lebid’

166-172
- PDF (Українська)
On uniform deviation from the space of continuous function

V. K. Maslyuchenko, V. S. Mel’nyk

173-181
- PDF (Українська)
Majorants of remainders of Taylor series of bounded holomorphic functions

I. Yu. Meremelya, V. V. Savchuk

182-188
- PDF (Українська)
Mean value theorem

E. I. Radzievskaya

189-195
- PDF (Русский)
Estimates of the entropy numbers and ε-entropy of the Nikol’skii-Besov classes of periodic functions of several variables

A. S. Romanyuk

196-213
- PDF (Русский)
Faber polynomials with common roots

V. V. Savchuk

214-227
- PDF (Українська)
Approximation by step-hyperbolic Fourier sums of classes $\mathbf{MB}^{\omega}_{1,\theta}(\bar{\gamma})$

S. A. Stasyuk

228-240
- PDF (Українська)
Estimates for the best approximations and approximation by Fourier sums of classes of convolutions of periodic functions of not high smoothness in integral metrics

T. A. Stepaniuk

241-269
- PDF (Українська)
Imbedding theorems for sets $L^{\psi}L_{M}$ and approximation by Fourier sums

S. O. Chaichenko

270-286
- PDF (Українська)
Order estimates of functionals in terms of which the best $n$-term approximations of classes ${\cal F}_{q,r}^{\psi}$ are expressed.

A. L. Shidlich

287-314
- PDF (Українська)
Best orthogonal trigonometric approximations of functions from classes $L_{\beta,1}^\psi$

V. V. Shkapa

315-329
- PDF (Українська)
Order estimates for approximative characteristics of functions from generalized classes of mixed smoothness of the Nikol’skii-Besov type

S. Ya. Yanchenko

330-343
- PDF (Українська)

Vol. 11 No. 3 (2014): Approximation Theory of Functions and Related Problems

Research papers

Lower bounds for Kolmogorov widths in classes of convolutions with Neumann kernel

On the best approximation by “angles” in the mean on the plane $\mathbb{R}^2$ with the Chebyshev-Hermite weight.

Padé approximants of series connected with bilinear transformations

On Lebesgue continuity on classes of $\bar{\psi}$-differentiable functions.

Two-dimensional Padé type approximants for some analytic functions of two variables

Construction of Padé approximants for Lauricella series by method of generalized moment representations

Solution of the Kolmogorov-Nikol’skii problem for three-harmonic Poisson integrals on classes $C^{\psi}_{\beta,\infty}$

Estimations of linear widths of the classes $H_p^\Omega$ periodic functions of many variables in the space $L_q$

Estimates of orthoprojection widths of classes $B^{\Omega}_{p,\theta}$ of periodic functions of several variables with given majorant of mixed moduli of continuity

Spectral analysis of two star graph with infinite chains

On uniform deviation from the space of continuous function

Majorants of remainders of Taylor series of bounded holomorphic functions

Mean value theorem

Estimates of the entropy numbers and ε-entropy of the Nikol’skii-Besov classes of periodic functions of several variables

Faber polynomials with common roots

Approximation by step-hyperbolic Fourier sums of classes $\mathbf{MB}^{\omega}_{1,\theta}(\bar{\gamma})$

Estimates for the best approximations and approximation by Fourier sums of classes of convolutions of periodic functions of not high smoothness in integral metrics

Imbedding theorems for sets $L^{\psi}L_{M}$ and approximation by Fourier sums

Order estimates of functionals in terms of which the best $n$-term approximations of classes ${\cal F}_{q,r}^{\psi}$ are expressed.

Best orthogonal trigonometric approximations of functions from classes $L_{\beta,1}^\psi$

Order estimates for approximative characteristics of functions from generalized classes of mixed smoothness of the Nikol’skii-Besov type

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