Characteristics of the linear and nonlinear approximations of the Nikol'skii-Besov-type classes of periodic functions of several variables

DOI10.1007/s10958-023-06602-yOpenAlexW4386049892MaRDI QIDQ6147570

Ihor A. Romanyuk, Svitlana Borysivna Hembars'ka, Oksana Volodymyrivna Fedunyk-Yaremchuk

Publication date: 1 February 2024

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-023-06602-y

zbMATH Keywords

widthsbest orthogonal trigonometric approximationsNikol'skii-Besov-type classes

Mathematics Subject Classification ID

Harmonic analysis in one variable (42Axx) Approximations and expansions (41Axx) Harmonic analysis in several variables (42Bxx)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Trigonometric widths of classes of periodic functions of many variables
• Best trigonometric approximations for some classes of periodic functions of several variables in the uniform metric
• Approximation of the classes \(B^{\omega}_{p,\theta}\) of periodic functions of several variables by polynomials with a spectrum in cubic domains
• The \(N\)-width for a generalized periodic Besov classes
• Estimates of entropy numbers and Gaussian measures for classes of functions with bounded mixed derivative
• Nonlinear approximation by trigonometric sums
• Order estimates for the best orthogonal trigonometric approximations of the classes of convolutions of periodic functions of low smoothness
• Entropy numbers and widths for the classes \(B_{p,\theta}^r\) of periodic functions of many variables
• Widths of the classes \( {B}_{p,\theta}^{\Omega } \) of periodic functions of many variables in the space \(B_{1,1}\)
• On the minimum of norms of mixed derivatives of trigonometric polynomials with given number of harmonics
• The infinite-dimensional widths and optimal recovery of generalized Besov classes
• On best \(m\)-term approximations and the entropy of sets in the space \(L^ 1\)
• Hyperbolic cross approximation. Lecture notes given at the courses on constructive approximation and harmonic analysis, Barcelona, Spain, May 30 -- June 3, 2016
• 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
• Estimates of approximating characteristics and the properties of the operators of best approximation for the classes of periodic functions in the space \(B_{1,1}\)
• Approximating characteristics of the classes of periodic multivariate functions in the space \(B_{ \infty , 1} \)
• The best approximations and widths of the classes of periodical functions of one and several variables in the space \(B_{\infty, 1}\)
• Kolmogorov widths of the classes \(B_{p,\theta}^\Omega\) of periodic functions of many variables in the space \(L_q\)
• Best trigonometric and bilinear approximations of classes of functions of several variables
• Über die beste Annäherung von Funktionen einer gegebenen Funktionenklasse
• Approximative characteristics of the isotropic classes of periodic functions of many variables
• Best M-Term trigonometric approximations of the classes $$ B_{p,\theta }^\Omega $$ of periodic functions of many variables
• Trigonometric and orthoprojection widths of classes of periodic functions of many variables
• Best orthogonal trigonometric approximations of the classes B Ω p,θ of periodic functions of many variables
• DIAMETERS OF SETS IN NORMED LINEAR SPACES AND THE APPROXIMATION OF FUNCTIONS BY TRIGONOMETRIC POLYNOMIALS
• Multivariate Approximation
• Best $ M$-term trigonometric approximations of Besov classes of periodic functions of several variables
• Best orthogonal trigonometric approximations of the Nikol'skii-Besov-type classes of periodic functions of one and several variables
• Approximative characteristics of the Nikol'skii-Besov-type classes of periodic functions in the space $B_{\infty,1}$
• Bilinear and trigonometric approximations of periodic functions of several variables of Besov classes $ B_{p, \theta}^r$
• Approximation of classes of periodic functions of several variables
• Characteristics of linear and nonlinear approximation of isotropic classes of periodic multivariate functions

This page was built for publication: Characteristics of the linear and nonlinear approximations of the Nikol'skii-Besov-type classes of periodic functions of several variables