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The Gelfand widths of lp-ball for 0 < p <= 1

Abstract : We provide sharp lower and upper bounds for the Gelfand widths of ℓ p -balls in the N -dimensional ℓ q N -space for 0 < p ≤ 1 and p < q ≤ 2 . Such estimates are highly relevant to the novel theory of compressive sensing, and our proofs rely on methods from this area.
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https://hal.inria.fr/hal-00766985
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Submitted on : Wednesday, December 19, 2012 - 12:15:45 PM
Last modification on : Saturday, January 15, 2022 - 4:14:29 AM

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Simon Foucart, Alain Pajor, Holger Rauhut, Tino Ullrich. The Gelfand widths of lp-ball for 0 < p <= 1. Journal of Complexity, Elsevier, 2010, 26 (6), pp.629 - 640. ⟨10.1016/j.jco.2010.04.004⟩. ⟨hal-00766985⟩

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