Entropy numbers of the Nikol'skii-Besov-type classes of periodic functions of many variables

DOI10.1007/s10958-019-04407-6zbMath1428.41032OpenAlexW2959381517MaRDI QIDQ2278236

Kateryna Pozharska

Publication date: 4 December 2019

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

Full work available at URL: https://doi.org/10.1007/s10958-019-04407-6

zbMATH Keywords

entropyentropy numbersmixed modulus of continuitystep hyperbolic cross

Mathematics Subject Classification ID

Function spaces arising in harmonic analysis (42B35) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46)

Related Items (2)

Estimates for the entropy numbers of the Nikol'skii–Besov classes of functions with mixed smoothness in the space of quasi‐continuous functions ⋮ Sharp estimates for the covering numbers of the Weierstrass fractal kernel

Cites Work

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• Estimation of the entropy numbers and Kolmogorov widths for the Nikol'skii-Besov classes of periodic functions of many variables
• An inequality for trigonometric polynomials and its application for estimating the entropy numbers
• 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
• Approximating characteristics of the classes of periodic multivariate functions in the space \(B_{ \infty , 1} \)
• Approximation of functions of several variables by trigonometric polynomials with given number of harmonics, and estimates of \(\epsilon\)- entropy
• Approximation characteristics of the classes B p,θ Ω of periodic functions of many variables
• Nonlinear approximations using sets of finite cardinality or finite pseudo-dimension
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