Cover Image

Approximative characteristics of the Nikol’skii – Besov classes of functions $S_{1, θ}^r B(\mathbb{R}^d)$

UDC 517.51 We establish the exact-order estimates for the approximation of the classes $S^{\boldsymbol{r}}_{1,\theta}B \left(\mathbb{R}^d\right)$ by entire functions of exponential type with supports of their Fourier transforms lying in a step hyperbolic cross. The error of approximation is estima...

Full description

Saved in:

Bibliographic Details
Date:	2026
Main Authors:	Radchenko, O. Ya., Yanchenko, S. Ya., Радченко, О. Я., Янченко, С. Я.
Format:	Article
Language:	Ukrainian
Published:	Institute of Mathematics, NAS of Ukraine 2026
Online Access:	https://umj.imath.kiev.ua/index.php/umj/article/view/1523
Tags:	Add Tag No Tags, Be the first to tag this record!
Journal Title:	Ukrains’kyi Matematychnyi Zhurnal
Download file:

Institution

Ukrains’kyi Matematychnyi Zhurnal

Similar Items

Best approximation of the functions from anisotropic Nikol’skii – Besov classes defined in $R^d$
by: Yanchenko, S. Ya., et al.
Published: (2018)

Approximation of Functions from the Isotropic Nikol’skii–Besov Classes in the Uniform and Integral Metrics
by: Yanchenko, S. Ya., et al.
Published: (2015)

Approximation of classes of periodic functions in one and many variables from the Nikol’skii – Besov and Sobolev spaces
by: Romanyuk, A. S., et al.
Published: (2022)

Approximative characteristics of the Nikol&#039;skii–Besov classes of functions S(ϒ 1,θ) B (ℝd)
by: Ya. Yanchenko, et al.
Published: (2019)

Kolmogorov widths of the Nikol’skii – Besov classes of periodic functions of many variables in the space of quasi-continuous functions
by: Romanyuk , A. S., et al.
Published: (2022)

Kolmogorov Widths for Analogs of the Nikol’skii–Besov Classes with Logarithmic Smoothness
by: Stasyuk, S. A., et al.
Published: (2015)

Approximation of the classes $S^r_{p,θ}B(\mathbb{R}^d)$ of functions of many variables by entire functions of a special form
by: Yanchenko, S. Ya., et al.
Published: (2010)

Trigonometric Widths of the Nikol’skii–Besov Classes in the Lebesgue Space with Mixed Norm
by: Akishev, G., et al.
Published: (2014)

Best approximation of the functions from anisotropic Nikol&#039;skii–Besov classes defined in Rd
by: Ya. Yanchenko
Published: (2018)

Order estimates of approximation characteristics of functions from the anisotropic Nikol&#039;skii-Besov classes
by: Ya. Yanchenko
Published: (2017)

Approximation of Functions from the Isotropic Nikol&#039;skii–Besov Classes in the Uniform and Integral Metrics
by: Ya. Yanchenko
Published: (2015)

Estimation of the Entropy Numbers and Kolmogorov Widths for the Nikol’skii–Besov Classes of Periodic Functions of Many Variables
by: Romanyuk, A. S., et al.
Published: (2015)

Best $m$-term trigonometric approximation for periodic functions with low mixed smoothness from the Nikol’skii – Besov-type classes
by: Stasyuk, S. A., et al.
Published: (2016)

Order estimates for approximative characteristics of functions from generalized classes of mixed smoothness of the Nikol&#039;skii-Besov type
by: Ya. Yanchenko
Published: (2014)

Approximation of classes of periodic functions in one and many variables from the Nikol&#039;skii–Besov and Sobolev spaces
by: A. S. Romaniuk, et al.
Published: (2022)

Kolmogorov widths of the Nikol&#039;skii–Besov classes of periodic functions of many variables in the space of quasicontinuous functions
by: A. S. Romaniuk, et al.
Published: (2022)

Approximations of classes $B^{Ω}_{p,θ}$ of functions of many variables by entire functions in the space $L_q (R^d)$
by: Yanchenko, S. Ya., et al.
Published: (2010)

Kolmogorov Widths for Analogs of the Nikol&#039;skii–Besov Classes with Logarithmic Smoothness
by: S. A. Stasjuk
Published: (2015)

Approximative characteristics and properties of operators of the best approximation of classes of functions from the Sobolev and Nikol&#039;skii-Besov spaces
by: A. S. Romaniuk, et al.
Published: (2020)

Bernstein – Nikol’skii-type inequalities for trigonometric polynomials with an arbitrary choice of harmonics
by: Vlasyk, H. M., et al.
Published: (2017)

Nikol’skii – Stechkin-type inequalities for the increments of trigonometric polynomials in metric spaces
by: Pichugov, S. A., et al.
Published: (2017)

Best bilinear approximations of functions from Nikolskii-Besov classes
by: Romanyuk, A. S., et al.
Published: (2012)

Characteristics of the linear and nonlinear approximations of the Nikol&#039;skii-Besov-type classes of periodic functions of several variables
by: S. B. Hembarska, et al.
Published: (2023)

Order estimates for the approximative characteristics of functions from the classes $S_{p,θ}^{Ω} B(R^d)$ with a given majorant of generalized mixed modules of smoothness in the uniform metric
by: Yanchenko, S. Ya., et al.
Published: (2016)

Trigonometric Widths of the Nikol&#039;skii–Besov Classes in the Lebesgue Space with Mixed Norm
by: G. Akishev
Published: (2014)

Best orthogonal trigonometric approximations of the Nikol&#039;skii–Besov-type classes of periodic functions in the space B∞,1
by: S. B. Hembarska, et al.
Published: (2022)

Best orthogonal trigonometric approximations of the Nikol'skii – Besov-type classes of periodic functions in the space $B_{\infty,1}$
by: Hembars’ka, S. B., et al.
Published: (2022)

Entropy numbers of the Nikol&#039;skii-Besov-type classes of periodic functions of many variables
by: K. V. Pozharska
Published: (2018)

Best m-term trigonometric approximation for periodic functions with low mixed smoothness from the Nikol&#039;skii – Besov-type classes
by: S. A. Stasiuk
Published: (2016)

Estimates of the entropy numbers and е-entropy of the Nikol&#039;skii-Besov classes of periodic functions of several variables
by: A. S. Romanjuk
Published: (2014)

Estimation of the Entropy Numbers and Kolmogorov Widths for the Nikol&#039;skii–Besov Classes of Periodic Functions of Many Variables
by: A. S. Romanjuk
Published: (2015)

Approximation of functions of the classes Srp,θ in the uniform metric
by: Ya. Yanchenko
Published: (2013)

Estimates for Approximation Characteristics of the Besov Classes $B_ r^{p,θ}$ of Periodic Functions of Many Variables in the Space $L_q. I$
by: Romanyuk, A. S., et al.
Published: (2001)

Approximation of Classes $B_{p,θ}^r$ by Linear Methods and Best Approximations
by: Romanyuk, A. S., et al.
Published: (2002)

Entropy numbers and Kolmogorov widths of Nikol&#039;skii-Besov classes of periodic functions of two variables in the space L∞
by: A. S. Romaniuk
Published: (2015)

On the Exponential Dichotomy on $\mathbb{R}$ of Linear Differential Equations in $\mathbb{R}^n$
by: Samoilenko, A. M., et al.
Published: (2001)

Localization of the Bochner-Riesz means in the Nikol'skii classes
by: Grona, V. L., et al.
Published: (1993)

Theorem on the existence of an invariant section over $\mathbb{R}^m$ for the indefinite monotone system in $\mathbb{R}^m \times \mathbb{R}^n$
by: Lagoda, V. A., et al.
Published: (2013)

Estimates for approximative characteristics of classes Sr(p,θ)B(Rd) of functions in the uniform metric
by: Ya. Yanchenko
Published: (2013)

Approximation characteristics of the Nikol&#039;sky-Besov-type classes of periodic single- and multivariable functions in the B_
by: S. B. Hembarska, et al.
Published: (2021)