V. N. Belykh, “On the absolute $\varepsilon$-entropy of some compact set of infinitely differentiable periodic functions”, Sibirsk. Mat. Zh., 52:3 (2011), 485–501; Siberian Math. J., 52:3 (2011), 381

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Sibirskii Matematicheskii Zhurnal, 2011, Volume 52, Number 3, Pages 485–501 (Mi smj2214)

This article is cited in 5 scientific papers (total in 5 papers)

On the absolute

ε

$\varepsilon$ -entropy of some compact set of infinitely differentiable periodic functions

V. N. Belykh

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Full-text PDF (355 kB) Citations (5)

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Abstract: We calculate the principal term of the asymptotics of the Kolmogorov

ε

$\varepsilon$ -entropy of some compact set of periodic infinitely differentiable functions that is continuously embedded into the space of continuous periodic functions.

Keywords:

ε

$\varepsilon$ -entropy, compact set, infinitely differentiable function, Gevrey class.

Received: 21.06.2010

English version:
Siberian Mathematical Journal, 2011, Volume 52, Issue 3, Pages 381–393
DOI: https://doi.org/10.1134/S0037446611030013

Bibliographic databases:

Document Type: Article

UDC: 517.518.222

Language: Russian

Citation: V. N. Belykh, “On the absolute

ε

$\varepsilon$ -entropy of some compact set of infinitely differentiable periodic functions”, Sibirsk. Mat. Zh., 52:3 (2011), 485–501; Siberian Math. J., 52:3 (2011), 381–393

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/smj2214

https://www.mathnet.ru/eng/smj/v52/i3/p485

This publication is cited in the following 5 articles:

V. N. Belykh, “Estimates of Alexandrov's $n$ -Width of the Compact Set of $C^{\infty}$ -Smooth Functions on a Finite Segment”, Sib Math J, 65:1 (2024), 1
V. N. Belykh, “Otsenki aleksandrovskogo $n$ -poperechnika kompakta $C^{\infty}$ -gladkikh funktsii na konechnom otrezke”, Sib. matem. zhurn., 65:1 (2024), 3–14
V. N. Belykh, “The absolute $\varepsilon$ -entropy of a compact set of infinitely differentiable aperiodic functions”, Siberian Math. J., 59:6 (2018), 947–959
Belykh V.N., “On Kolmogorov'S Epsilon-Entropy For a Compact Set of Infinitely Differentiable Aperiodic Functions (Babenko'S Problem)”, Dokl. Math., 98:2 (2018), 416–420
Belykh V.N., “Estimates of Kolmogorov's E >-Entropy for Compact Sets of Infinitely Differentiable Aperiodic Functions (Babenko's Problem)”, Dokl. Math., 88:2 (2013), 503–507

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Full-text PDF :	119
References:	68
First page:	10

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