Lower Bounds for n-Term Approximations of Plane Convex Sets and Related Topics |
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| Authors: | Kashin B S |
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| Institution: | (1) V. A. Steklov Mathematics Institute, Russian Academy of Sciences, Russia |
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| 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  , these bounds cannot decrease more rapidly than
. |
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| Keywords: | n-term approximation plane convex set Haar system orthonormal system Hilbert space Walsh system |
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