{
  "id": "1606.00738",
  "version": "v1",
  "published": "2016-06-02T16:03:43.000Z",
  "updated": "2016-06-02T16:03:43.000Z",
  "title": "Product of octahedra is badly approximated in the $\\ell_{2,1}$-metric",
  "authors": [
    "Yu. V. Malykhin",
    "K. S. Ryutin"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "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).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-02T16:03:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cartesian product",
      "half-dimensional subspaces",
      "linear widths",
      "parameter space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}