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The Gelfand widths of $\ell_p$-balls for $0<p\leq 1$

Published 3 Feb 2010 in math.FA, cs.IT, and math.IT | (1002.0672v2)

Abstract: We provide sharp lower and upper bounds for the Gelfand widths of $\ell_p$-balls in the $N$-dimensional $\ell_qN$-space for $0<p\leq 1$ and $p<q \leq 2$. 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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