Cover Image

Best Linear Methods of Approximation of Functions of the Hardy Class $H_p$

We determine the exact value of the best linear polynomial approximation of a unit ball of the Hardy space $H_p, 1 ≤ p ≤ ∞$, on concentric circles $Tρ = z ∈ C:|z|=ρ, 0 ≤ ρ < 1$, in the uniform metric. We construct the best linear method of approximation and prove the uniqueness of this method...

Full description

Saved in:

Bibliographic Details
Date:	2003
Main Authors:	Savchuk, V. V., Савчук, В. В.
Format:	Article
Language:	Ukrainian English
Published:	Institute of Mathematics, NAS of Ukraine 2003
Online Access:	https://umj.imath.kiev.ua/index.php/umj/article/view/3967
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 linear methods of approximation and optimal orthonormal systems of the Hardy space
by: Savchuk, V. V., et al.
Published: (2008)

Best linear methods for the approximation of functions of the Bergman class by algebraic polynomials
by: Savchuk, V. V., et al.
Published: (2006)

Approximation of the Classes $H_p^{Ω}$ of Periodic Functions of Many Variables in the Space $L_p$
by: Derev’yanko, N. V., et al.
Published: (2014)

Best approximation by holomorphic functions. Application to the best polynomial approximation of classes of holomorphic functions
by: Savchuk, V. V., et al.
Published: (2007)

Linear approximation methods and the best approximations of the Poisson integrals of functions from the classes $H_{ω_p}$ in the metrics of the spaces $L_p$
by: Serdyuk, A. S., et al.
Published: (2010)

On the best approximation of the HЁolder classes by linear methods
by: D. S. Skorokhodov
Published: (2014)

On the Best Linear Approximation Method for Hцlder Classes
by: D. S. Skorokhodov
Published: (2015)

On integral representations in the Hardi classes and on the best approximations in some functional spaces
by: Dovgoshei , A. A., et al.
Published: (1991)

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

On the Best Linear Approximation Method for Hölder Classes
by: Skorokhodov, D. S., et al.
Published: (2015)

Linear methods for approximation of some classes of holomorphic functions from the Bergman space
by: Savchuk, V. V., et al.
Published: (2008)

Approximation of the Classes HpΩ of Periodic Functions of Many Variables in the Space Lp
by: N. V. Derevianko
Published: (2014)

Best approximation of reproducing kernels of spaces of analytic functions
by: Savchuk, V. V., et al.
Published: (2004)

Norms of Multipliers and Best Approximations of Holomorphic Functions of Many Variables
by: Savchuk, V. V., et al.
Published: (2002)

On a boundary properties of functions from a class Hp(p ≥ 1)
by: U. Hrabova, et al.
Published: (2022)

Approximation by fourier sums and best approximations on classes of analytic functions
by: Serdyuk, A. S., et al.
Published: (2000)

On the embedding of Waterman class in the class Hpω
by: Goginava, U., et al.
Published: (2005)

Best Bilinear Approximations for the Classes of Functions of Many Variables
by: Romanyuk, A. S., et al.
Published: (2013)

On the Best Linear Methods of Approximation and the Exact Values of Widths for Some Classes of Analytic Functions in the Weighted Bergman Space
by: M. R. Langarshoev
Published: (2015)

On the Best Linear Methods of Approximation and the Exact Values of Widths for Some Classes of Analytic Functions in the Weighted Bergman Space
by: Langarshoev, M. R., et al.
Published: (2015)

Estimates for the best asymmetric approximations of asymmetric classes of functions
by: Motornyi, V. P., et al.
Published: (2011)

Best Bilinear Approximations for the Classes of Functions of Many Variables
by: A. S. Romanjuk, et al.
Published: (2013)

Best bilinear approximations of the classes $S^{\Omega}_{p, \theta}B$ of periodic functions of many variables
by: Solich, K. V., et al.
Published: (2011)

The Best Approximation of Function Classes Generated by Composite Kernels
by: Сорич, Віктор, et al.
Published: (2025)

Widths and best approximations for classes of convolutions of periodic functions
by: Serdyuk, A. S., et al.
Published: (1999)

Approximation of holomorphic functions of Zygmund class by Fejer means
by: Savchuk, V. V., et al.
Published: (2012)

Best approximation by ridge functions in $L_p$-spaces
by: Maiorov, V. E., et al.
Published: (2010)

The best approximations of the classes of functions preset by means of the continuity modulus
by: Babenko , V. F., et al.
Published: (1992)

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

Best approximation of periodic functions of several variables from the classes $MB^{\omega}_{p,\theta}$
by: Stasyuk, S. A., et al.
Published: (2012)

Best Orthogonal Trigonometric Approximations of Classes of Functions of Many Variables $L^{ψ}_{β, p}$
by: Konsevich, N. M., et al.
Published: (2001)

Asymptotic behavior of the best approximations for the functions in $L_p$
by: Pichugov, S. A., et al.
Published: (1993)

On the best approximation of classes of convolutions of periodic functions by trigonometric polynomials
by: Serdyuk, A. S., et al.
Published: (1995)

On the Exact Asymptotics of the Best Relative Approximations of Classes of Periodic Functions by Splines
by: Parfinovych, N. V., et al.
Published: (2001)

Approximation by linear methods of classes of (ш,в)−differentiable functions
by: A. S. Serdiuk, et al.
Published: (2013)

Best approximations of the Cauchy – Szegö kernel in the mean on the unit circle
by: Savchuk, V. V., et al.
Published: (2018)

Lower bounds for the deviations of the best linear methods of approximation of continuous functions by trigonometric polynomials
by: Pichugov, S. A., et al.
Published: (2012)

Best $m$-term trigonometric approximation for the classes $B^r_{p,θ}$ of functions of low smoothness
by: Stasyuk, S. A., et al.
Published: (2010)

Best orthogonal trigonometric approximations of the classes $B^{Ω}_{p,θ}$ of periodic functions of many variables
by: Voitenko, S. P., et al.
Published: (2009)

Best approximations of the classes $B_{p,\,\theta}^{r}$ of periodic functions of many variables in uniform metric
by: Romanyuk, A. S., et al.
Published: (2006)