Asymptotics of Kolmogorov's \(\varepsilon \)-entropy for some classes of infinitely differentiable periodic functions (Babenko's problem)

DOI10.1134/S1064562410020365zbMath1211.42001MaRDI QIDQ606579

Vladimir N. Belykh

Publication date: 17 November 2010

Published in: Doklady Mathematics (Search for Journal in Brave)

zbMATH Keywords

asymptoticsGevrey class\(\varepsilon\)-netinfinitely differentiable periodic functions\(\varepsilon\)-entropy of Kolmogorovmost economical covering of compact setproblem of Babenko

Mathematics Subject Classification ID

Trigonometric approximation (42A10) Numerical methods for trigonometric approximation and interpolation (65T40) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46) Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.) (42A32)

Related Items (4)

Estimates of Kolmogorov's \(\varepsilon\)-entropy for compact sets of infinitely differentiable aperiodic functions (Babenko's problem) ⋮ On the absolute \(\varepsilon \)-entropy of some compact set of infinitely differentiable periodic functions ⋮ The absolute \({\varepsilon}\)-entropy of a compact set of infinitely differentiable aperiodic functions ⋮ An unsaturated numerical method for the exterior axisymmetric Neumann problem for Laplace's equation

Cites Work

• Exterior axisymmetric Neumann problem for the Laplace equation: Numerical algorithms without saturation
• Rational approximation and \(n\)-dimensional diameter
• On the representation of analytic functions by infinite series

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