Estimates of approximating characteristics and the properties of the operators of best approximation for the classes of periodic functions in the space \(B_{1,1}\)

DOI10.1007/s11253-022-01990-xzbMath1498.41027OpenAlexW4210398003MaRDI QIDQ2116167

A. S. Romanyuk, Sergii Ya. Yanchenko

Publication date: 16 March 2022

Published in: Ukrainian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11253-022-01990-x

Mathematics Subject Classification ID

Function spaces arising in harmonic analysis (42B35) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Best approximation, Chebyshev systems (41A50) Approximation by operators (in particular, by integral operators) (41A35) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46)

Related Items (4)

Characteristics of the linear and nonlinear approximations of the Nikol'skii-Besov-type classes of periodic functions of several variables ⋮ Kolmogorov widths of the Nikol'skii-Besov classes of periodic functions of many variables in the space of quasicontinuous functions ⋮ Best orthogonal trigonometric approximations of the Nikol'skii-Besov-type classes of periodic functions in the space \(B_{ \infty ,1}\) ⋮ Approximation of the classes of periodic functions of one and many variables from the Nikol'skii-Besov and Sobolev spaces

Cites Work

• Diameters and best approximation of the classes \(B^r_{p,\theta}\) of periodic functions of several variables
• Estimates of the Fourier widths of the classes of periodic functions with given majorant of the mixed modulus of smoothness
• Approximation of classes of periodic functions of several variables by nuclear operators
• Spaces of functions of mixed smoothness from the decomposition point of view
• Entropy numbers and widths for the classes \(B_{p,\theta}^r\) of periodic functions of many variables
• Wavelet approximation and Fourier widths of classes of periodic functions of several variables. II
• Estimates of the Fourier widths of classes of Nikol'skii-Besov and Lizorkin-Triebel types of periodic functions of several variables
• Hyperbolic cross approximation. Lecture notes given at the courses on constructive approximation and harmonic analysis, Barcelona, Spain, May 30 -- June 3, 2016
• Estimation of some approximating characteristics of the classes of periodic functions of one and many variables
• Approximating characteristics of the classes of periodic multivariate functions in the space \(B_{ \infty , 1} \)
• On the widths of multivariate periodic classes of functions whose mixed moduli of continuity are bounded by a product of power- and logarithmic-type functions
• Approximation characteristics of the classes B p,θ Ω of periodic functions of many variables
• Best approximations and widths of classes of periodic functions of several variables
• Approximability of the classes $ B_{p,\theta}^r$ of periodic functions of several variables by linear methods and best approximations
• On the Order of the Trigonometric Diameter of the Anisotropic Nikol’skii–Besov Class in the Metric of Anisotropic Lorentz Spaces
• Estimates of approximative characteristics of the classes $B^{\Omega}_{p,\theta}$ of periodic functions of several variables with given majorant of mixed moduli of continuity in the space $L_{q}$
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Estimates of approximating characteristics and the properties of the operators of best approximation for the classes of periodic functions in the space \(B_{1,1}\)