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Mat. Zametki, 2002, Volume 72, Issue 4, Pages 509–515 (Mi mz440)  

This article is cited in 3 scientific papers (total in 3 papers)

Lower Bounds for $n$-Term Approximations of Plane Convex Sets and Related Topics

B. S. Kashin

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: In this paper, we establish lower bounds for $n$-term approximations in the metric of$L^2(I^2)$ of characteristic functions of plane convex subsets of the square $I^2$ with respect to arbitrary orthogonal systems. It is shown that, as $n\to \infty $, these bounds cannot decrease more rapidly than $1/n$.

DOI: https://doi.org/10.4213/mzm440

Full text: PDF file (205 kB)
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English version:
Mathematical Notes, 2002, 72:4, 473–478

Bibliographic databases:

UDC: 517.5
Received: 30.04.2002

Citation: B. S. Kashin, “Lower Bounds for $n$-Term Approximations of Plane Convex Sets and Related Topics”, Mat. Zametki, 72:4 (2002), 509–515; Math. Notes, 72:4 (2002), 473–478

Citation in format AMSBIB
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\by B.~S.~Kashin
\paper Lower Bounds for $n$-Term Approximations of Plane Convex Sets and Related Topics
\jour Mat. Zametki
\yr 2002
\vol 72
\issue 4
\pages 509--515
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\crossref{https://doi.org/10.4213/mzm440}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1963146}
\zmath{https://zbmath.org/?q=an:1051.41013}
\transl
\jour Math. Notes
\yr 2002
\vol 72
\issue 4
\pages 473--478
\crossref{https://doi.org/10.1023/A:1020528210992}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0141848652}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. P. G. Grigor'ev, “On the Orthomassivity of the Set of Characteristic Functions of Convex Sets”, Math. Notes, 75:1 (2004), 140–144  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. B. S. Kashin, “Remark on Estimates of Orthomassivity”, Math. Notes, 84:6 (2008), 879–882  mathnet  crossref  crossref  mathscinet  isi
    3. B. S. Kashin, Yu. V. Malykhin, K. S. Ryutin, “Kolmogorov width and approximate rank”, Proc. Steklov Inst. Math., 303 (2018), 140–153  mathnet  crossref  crossref  mathscinet  isi  elib
  • Математические заметки Mathematical Notes
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