arxiv: 1002.0672 · v2 · pith:3KLIITXAnew · submitted 2010-02-03 · 🧮 math.FA · cs.IT· math.IT

The Gelfand widths of ell_p-balls for 0<pleq 1

Simon Foucart , Alain Pajor , Holger Rauhut , Tino Ullrich This is my paper

classification 🧮 math.FA cs.ITmath.IT

keywords ballsgelfandwidthsareaboundscompressivedimensionalestimates

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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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The Gelfand widths of ell_p-balls for 0<pleq 1

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