Mathematical Notes

, Volume 72, Issue 3–4, pp 473–478 | Cite as

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

  • B. S. Kashin
Article
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Abstract

In this paper, we establish lower bounds for n-term approximations in the metric of L2(I2) of characteristic functions of plane convex subsets of the square I2 with respect to arbitrary orthogonal systems. It is shown that, as n→∞, these bounds cannot decrease more rapidly than \(1/n\).

n-term approximation plane convex set Haar system orthonormal system Hilbert space Walsh system 

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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • B. S. Kashin
    • 1
  1. 1.V. A. Steklov Mathematics InstituteRussian Academy of SciencesRussia

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