{
  "id": "1811.09892",
  "version": "v1",
  "published": "2018-11-24T20:20:49.000Z",
  "updated": "2018-11-24T20:20:49.000Z",
  "title": "Asymptotics of determinants for finite sections of operators with almost periodic diagonals",
  "authors": [
    "Torsten Ehrhardt",
    "Zheng Zhou"
  ],
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "Let $A = (a_{j,k})_{j,k=-\\infty}^\\infty$ be a bounded linear operator on $l^2(\\mathbb{Z})$ whose diagonals $D_n(A) = (a_{j,j-n})_{j=-\\infty}^\\infty\\in l^\\infty(\\mathbb{Z})$ are almost periodic sequences. For certain classes of such operators and under certain conditions, we are going to determine the asymptotics of the determinants $\\det A_{n_1,n_2}$ of the finite sections of the operator $A$ as their size $n_2 - n_1$ tends to infinity. Examples of such operators include block Toeplitz operators and the almost Mathieu operator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-24T20:20:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B35",
      "47B36",
      "47B37",
      "47L80"
    ],
    "keywords": [
      "finite sections",
      "periodic diagonals",
      "asymptotics",
      "determinants",
      "block toeplitz operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}