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Matematicheskie Zametki, 2017, Volume 101, Issue 1, Pages 85–90
DOI: https://doi.org/10.4213/mzm11281
(Mi mzm11281)
 

This article is cited in 14 scientific papers (total in 14 papers)

The Product of Octahedra is Badly Approximated in the $\ell_{2,1}$-Metric

Yu. V. Malykhina, K. S. Ryutinb

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Lomonosov Moscow State University
References:
Abstract: We prove that the Cartesian product of octahedra $B_{1,\infty}^{n,m}=B_1^n\times \dots\times B_1^n$ ($m$ factors) is poorly approximated by spaces of half dimension in the mixed norm: $d_{N/2}(B_{1,\infty}^{n,m},\ell_{2,1}^{n,m})\ge cm$, $N=mn$. As a corollary, we find the order of linear widths of the Hölder–Nikolskii classes $H^r_p(\mathbb T^d)$ in the metric of $L_q$ in certain domains of variation of the parameters $(p,q)$.
Keywords: Kolmogorov width, vector balancing.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00332
This work was supported by the Russian Foundation for Basic Research under grant 14-01-00332.
Received: 09.06.2016
English version:
Mathematical Notes, 2017, Volume 101, Issue 1, Pages 94–99
DOI: https://doi.org/10.1134/S0001434617010096
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: Yu. V. Malykhin, K. S. Ryutin, “The Product of Octahedra is Badly Approximated in the $\ell_{2,1}$-Metric”, Mat. Zametki, 101:1 (2017), 85–90; Math. Notes, 101:1 (2017), 94–99
Citation in format AMSBIB
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\pages 85--90
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  • https://doi.org/10.4213/mzm11281
  • https://www.mathnet.ru/eng/mzm/v101/i1/p85
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    This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Математические заметки Mathematical Notes
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