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arXiv · 1002.0672

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

Simon Foucart·Alain Pajor·Holger Rauhut·Tino Ullrich
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Abstract

We provide sharp lower and upper bounds for the Gelfand widths of $\ell_p$-balls in the $N$-dimensional $\ell_q^N$-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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Simon Foucart, Alain Pajor, Holger Rauhut, Tino Ullrich. 2010-02-03. The Gelfand widths of $\ell_p$-balls for $0<p\leq 1$. https://doi.org/10.1016/j.jco.2010.04.004

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