{
  "id": "1501.07876",
  "version": "v1",
  "published": "2015-01-30T18:39:37.000Z",
  "updated": "2015-01-30T18:39:37.000Z",
  "title": "Commutation Relations for Unitary Operators II",
  "authors": [
    "M. A. Astaburuaga",
    "O. Bourget",
    "V. H. Cortés"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $f$ be a regular non-constant symbol defined on the $d$-dimensional torus ${\\mathbb T}^d$ with values on the unit circle. Denote respectively by $\\kappa$ and $L$, its set of critical points and the associated Laurent operator on $l^2({\\mathbb Z}^d)$. Let $U$ be a suitable unitary local perturbation of $L$. We show that the operator $U$ has finite point spectrum and no singular continuous component away from the set $f(\\kappa)$. We apply these results and provide a new approach to analyze the spectral properties of GGT matrices with asymptotically constant Verblunsky coefficients. The proofs are based on positive commutator techniques. We also obtain some propagation estimates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-30T18:39:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "unitary operators",
      "commutation relations",
      "asymptotically constant verblunsky coefficients",
      "singular continuous component away",
      "finite point spectrum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150107876A"
    }
  }
}