{
  "id": "math-ph/9910017",
  "version": "v1",
  "published": "1999-10-12T17:09:48.000Z",
  "updated": "1999-10-12T17:09:48.000Z",
  "title": "Uniform spectral properties of one-dimensional quasicrystals, III. $α$-continuity",
  "authors": [
    "David Damanik",
    "Rowan Killip",
    "Daniel Lenz"
  ],
  "comment": "12 pages",
  "doi": "10.1007/s002200000203",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the spectral properties of discrete one-dimensional Schr\\\"odinger operators with Sturmian potentials. It is shown that the point spectrum is always empty. Moreover, for rotation numbers with bounded density, we establish purely $\\alpha$-continuous spectrum, uniformly for all phases. The proofs rely on the unique decomposition property of Sturmian potentials, a mass-reproduction technique based upon a Gordon-type argument, and on the Jitomirskaya-Last extension of the Gilbert-Pearson theory of subordinacy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-10-12T17:09:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q10",
      "47B80"
    ],
    "keywords": [
      "uniform spectral properties",
      "one-dimensional quasicrystals",
      "sturmian potentials",
      "continuity",
      "unique decomposition property"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Communications in Mathematical Physics",
      "year": 2000,
      "volume": 212,
      "number": 1,
      "pages": 191
    },
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000CMaPh.212..191D"
    }
  }
}