Estimation of the entropy numbers and Kolmogorov widths for the Nikol'skii-Besov classes of periodic functions of many variables

DOI10.1007/s11253-016-1186-5zbMath1388.46028OpenAlexW2399096136MaRDI QIDQ1699445

A. S. Romanyuk

Publication date: 23 February 2018

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

Full work available at URL: https://doi.org/10.1007/s11253-016-1186-5

zbMATH Keywords

entropy numbersKolmogorov widthsNikol'skii-Besov classes

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

Related Items (10)

Entropy numbers of finite dimensional mixed-norm balls and function space embeddings with small mixed smoothness ⋮ Estimates for the entropy numbers of the Nikol'skii–Besov classes of functions with mixed smoothness in the space of quasi‐continuous functions ⋮ On the entropy numbers between the anisotropic spaces and the spaces of functions with mixed smoothness ⋮ Entropy numbers and widths for the classes \(B_{p,\theta}^r\) of periodic functions of many variables ⋮ Kolmogorov widths and entropy numbers in the Orlicz spaces with Luxembourg norm ⋮ Widths of the classes \( {B}_{p,\theta}^{\Omega } \) of periodic functions of many variables in the space \(B_{1,1}\) ⋮ Entropy numbers of the Nikol'skii-Besov-type classes of periodic functions of many variables ⋮ Estimates for the entropy numbers of the classes \( {B}_{p,\theta}^{\Omega } \) of periodic multivariable functions in the uniform metric ⋮ Kolmogorov widths of the Nikol'skii-Besov classes of periodic functions of many variables in the space of quasicontinuous functions ⋮ Estimation of some approximating characteristics of the classes of periodic functions of one and many variables

Cites Work

• An inequality for the entropy numbers and its application
• Spaces of functions of mixed smoothness from the decomposition point of view
• Entropy numbers, s-numbers, and eigenvalue problems
• Approximation of the Besov classes of periodic functions of several variables in the space \(L_ q\)
• Estimates of entropy numbers and Gaussian measures for classes of functions with bounded mixed derivative
• On best \(m\)-term approximations and the entropy of sets in the space \(L^ 1\)
• Estimate of approximate characteristics for classes of functions with bounded mixed derivative
• Approximation of functions of several variables by trigonometric polynomials with given number of harmonics, and estimates of \(\epsilon\)- entropy
• Subspaces of Small Codimension of Finite-Dimensional Banach Spaces
• Approximability of the classes $ B_{p,\theta}^r$ of periodic functions of several variables by linear methods and best approximations
• PIECEWISE-POLYNOMIAL APPROXIMATIONS OF FUNCTIONS OF THE CLASSES $ W_{p}^{\alpha}$
• Nonlinear approximations using sets of finite cardinality or finite pseudo-dimension
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• 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: Estimation of the entropy numbers and Kolmogorov widths for the Nikol'skii-Besov classes of periodic functions of many variables