{
  "id": "2011.09411",
  "version": "v1",
  "published": "2020-11-18T17:14:45.000Z",
  "updated": "2020-11-18T17:14:45.000Z",
  "title": "Sign intermixing for Riesz bases and frames measured in the Kantorovich-Rubinstein norm",
  "authors": [
    "Nikolai Nikolski",
    "Alexander Volberg"
  ],
  "comment": "16 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "We measure a sign interlacing phenomenon for Bessel sequences $ (u_{k})$ in $ L^{2}$ spaces in terms of the Kantorovich--Rubinstein mass moving norm $ \\Vert u_{k}\\Vert _{KR}$. Our main observation shows that, quantitatively, the rate of the decreasing $ \\Vert u_{k}\\Vert _{KR}\\longrightarrow 0$ havily depends on S. Bernstein $ n$-widths of a compact of Lipschitz functions. In particular, it depends on the dimension of the measure space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-18T17:14:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B35",
      "F.2.2"
    ],
    "keywords": [
      "riesz bases",
      "kantorovich-rubinstein norm",
      "sign intermixing",
      "kantorovich-rubinstein mass moving norm",
      "sign interlacing phenomenon"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}