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

Functional Analysis 2010-12-17 v2 Information Theory math.IT

Abstract

We provide sharp lower and upper bounds for the Gelfand widths of p\ell_p-balls in the NN-dimensional qN\ell_q^N-space for 0<p10<p\leq 1 and p<q2p<q \leq 2. Such estimates are highly relevant to the novel theory of compressive sensing, and our proofs rely on methods from this area.

Keywords

Cite

@article{arxiv.1002.0672,
  title  = {The Gelfand widths of $\ell_p$-balls for $0<p\leq 1$},
  author = {Simon Foucart and Alain Pajor and Holger Rauhut and Tino Ullrich},
  journal= {arXiv preprint arXiv:1002.0672},
  year   = {2010}
}

Comments

15 pages