{"paper":{"title":"Product of octahedra is badly approximated in the $\\ell_{2,1}$-metric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"K.S. Ryutin, Yu.V. Malykhin","submitted_at":"2016-06-02T16:03:43Z","abstract_excerpt":"We prove that the cartesian product of octahedra $B_{1,\\infty}^{n,m}=B_1^n\\times\\ldots\\times B_1^n$ ($m$ octahedra) is badly approximated by half--dimensional subspaces in mixed--norm: $d_{N/2}(B_{1,\\infty}^{n,m},\\ell_{2,1}^{n,m})\\ge cm$, $N=mn$. As a corollary the orders for linear widths of H\\\"older--Nikolskii classes $H^r_p(\\mathbb T^d)$ in the $L_q$ metric are obtained for $(p,q)$ in a certain set (a domain in the parameter space)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00738","kind":"arxiv","version":1},"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"}