This is an announcement for the paper "The Gelfand widths of $\ell_p$-balls for $0<p\leq 1$" by Simon Foucart, Alain Pajor, Holger Rauhut, and Tino Ullrich.

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.

Archive classification: math.FA cs.IT math.IT

Mathematics Subject Classification: 41A46, 46B09

Remarks: 15 pages

The source file(s), GelfandSAHTarxiv.tex: 45830 bytes, is(are) stored in gzipped form as 1002.0672.gz with size 15kb. The corresponding postcript file has gzipped size 84kb.

Submitted from: tino.ullrich@hcm.uni-bonn.de

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