{
  "id": "1801.07228",
  "version": "v1",
  "published": "2018-01-22T18:18:36.000Z",
  "updated": "2018-01-22T18:18:36.000Z",
  "title": "Scattering the geometry of weighted graphs",
  "authors": [
    "Batu Güneysu",
    "Matthias Keller"
  ],
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "Given two weighted graphs $(X,b_k,m_k)$, $k=1,2$ with $b_1\\sim b_2$ and $m_1\\sim m_2$, we prove a weighted $L^1$-criterion for the existence and completeness of the wave operators $ W_{\\pm}(H_{2},H_1, I_{1,2})$, where $H_k$ denotes the natural Laplacian in $\\ell^2(X,m_k)$ w.r.t. $(X,b_k,m_k)$ and $I_{1,2}$ the trivial identification of $\\ell^2(X,m_1)$ with $\\ell^2(X,m_2)$. In particular, this entails a very general criterion for the absolutely continuous spectra of $H_1$ and $H_2$ to be equal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-22T18:18:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weighted graphs",
      "natural laplacian",
      "general criterion",
      "trivial identification",
      "scattering"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}