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

Simon Foucart, Alain Pajor, Holger Rauhut, Tino Ullrich

Published 2010-02-03, updated 2010-12-16Version 2

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.