{"paper":{"title":"The Gelfand widths of $\\ell_p$-balls for $0<p\\leq 1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.FA","authors_text":"Alain Pajor, Holger Rauhut, Simon Foucart, Tino Ullrich","submitted_at":"2010-02-03T09:20:52Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.0672","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}