{
  "id": "1009.3694",
  "version": "v1",
  "published": "2010-09-20T05:00:19.000Z",
  "updated": "2010-09-20T05:00:19.000Z",
  "title": "Continuity of spectral averaging",
  "authors": [
    "C. A. Marx"
  ],
  "journal": "Proc. Math. Soc., posted on August 20, 2010, PII S 0002-9939(2010)10629-9",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider averages $\\kappa$ of spectral measures of rank one perturbations with respect to a $\\sigma$-finite measure $\\nu$. It is examined how various degrees of continuity of $\\nu$ with respect to $\\alpha$-dimensional Hausdorff measures ($0 \\leq \\alpha \\leq 1$) are inherited by $\\kappa$. This extends Kotani's trick where $\\nu$ is simply the Lebesgue measure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-09-20T05:00:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q10",
      "81Q15",
      "47B15",
      "47B36",
      "47B80"
    ],
    "keywords": [
      "spectral averaging",
      "continuity",
      "extends kotanis trick",
      "dimensional hausdorff measures",
      "finite measure"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.3694M"
    }
  }
}