Yu. N. Subbotin, S. A. Telyakovskii, “On the Equality of Kolmogorov and Relative Widths of Classes of Differentiable Functions”, Mat. Zametki, 86:3 (2009), 456–465; Math. Notes, 86:3 (2009), 432

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Matematicheskie Zametki, 2009, Volume 86, Issue 3, Pages 456–465
DOI: https://doi.org/10.4213/mzm6330 (Mi mzm6330)

This article is cited in 2 scientific papers (total in 4 papers)

On the Equality of Kolmogorov and Relative Widths of Classes of Differentiable Functions

Yu. N. Subbotin^a, S. A. Telyakovskii^b

^a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
^b Steklov Mathematical Institute, Russian Academy of Sciences

Full-text PDF (401 kB) Citations (4)

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DOI: https://doi.org/10.4213/mzm6330

Abstract: We obtain sharper estimates of the remainders in the expression for the least value of the multiplier

M

$M$ for which the Kolmogorov widths

d_{n} (W_{C}^{r}, C)

$d_n(W_C^r,C)$ and the relative widths

K_{n} (W_{C}^{r}, M W_{C}^{j}, C)

$K_n(W_C^r,MW_C^j,C)$ of the class

W_{C}^{r}

$W_C^r$ with respect to the class

M W_{C}^{j}

$MW_C^j$ ,

j < r

$j<r$ , where

r - j

$r-j$ is odd, are equal.

Keywords: Kolmogorov width, relative width of a class, differentiable function,

2 π

$2\pi$ -periodic function, Banach space, Favard constant.

Received: 18.09.2008

English version:
Mathematical Notes, 2009, Volume 86, Issue 3, Pages 432–439
DOI: https://doi.org/10.1134/S0001434609090168

Bibliographic databases:

Document Type: Article

UDC: 517.224

Language: Russian

Citation: Yu. N. Subbotin, S. A. Telyakovskii, “On the Equality of Kolmogorov and Relative Widths of Classes of Differentiable Functions”, Mat. Zametki, 86:3 (2009), 456–465; Math. Notes, 86:3 (2009), 432–439

Citation in format AMSBIB

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\paper On the Equality of Kolmogorov and Relative Widths of Classes of Differentiable Functions

\jour Mat. Zametki

\yr 2009

\vol 86

\issue 3

\pages 456--465

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\crossref{https://doi.org/10.4213/mzm6330}

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\zmath{https://zbmath.org/?q=an:1192.46023}

\transl

\jour Math. Notes

\yr 2009

\vol 86

\issue 3

\pages 432--439

\crossref{https://doi.org/10.1134/S0001434609090168}

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Linking options:

https://www.mathnet.ru/eng/mzm6330

https://doi.org/10.4213/mzm6330

https://www.mathnet.ru/eng/mzm/v86/i3/p456

Erratum

Letter to the Editor
Yu. N. Subbotin, S. A. Telyakovskii
Mat. Zametki, 2010, 87:3, 480

This publication is cited in the following 4 articles:

S. P. Sidorov, “Linear Relativen-Widths for Linear Operators Preserving an Intersection of Cones”, International Journal of Mathematics and Mathematical Sciences, 2014 (2014), 1
Gocheva-Ilieva S.G., Feschiev I.H., “New Recursive Representations for the Favard Constants with Application to Multiple Singular Integrals and Summation of Series”, Abstract Appl. Anal., 2013, 523618
“Yurii Nikolaevich Subbotin. (K semidesyatipyatiletiyu so dnya rozhdeniya)”, Tr. IMM UrO RAN, 17, no. 3, 2011, 8–13
Yu. N. Subbotin, S. A. Telyakovskii, “Letter to the Editor”, Math. Notes, 87:3 (2010), 452–452

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

Statistics & downloads:
Abstract page:	520
Full-text PDF :	204
References:	81
First page:	19

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