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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
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.
Received: 09.06.2016
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
Linking options:
https://www.mathnet.ru/eng/mzm11281https://doi.org/10.4213/mzm11281 https://www.mathnet.ru/eng/mzm/v101/i1/p85
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Abstract page: | 715 | Full-text PDF : | 91 | References: | 51 | First page: | 30 |
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