{
  "id": "1702.00965",
  "version": "v1",
  "published": "2017-02-03T10:36:02.000Z",
  "updated": "2017-02-03T10:36:02.000Z",
  "title": "Asymptotic Eigenfunctions for a class of Difference Operators",
  "authors": [
    "Markus Klein",
    "Elke Rosenberger"
  ],
  "journal": "Asymptotic Analysis 73, p. 1-36 (2011)",
  "doi": "10.3233/ASY-2010-1025",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "We analyze a general class of difference operators $H_\\varepsilon = T_\\varepsilon + V_\\varepsilon$ on $\\ell^2(\\varepsilon \\mathbb{Z}^d)$, where $V_\\varepsilon$ is a one-well potential and $\\varepsilon$ is a small parameter. We construct formal asymptotic expansions of WKB-type for eigenfunctions associated with the low lying eigenvalues of $H_\\varepsilon$. These are obtained from eigenfunctions or quasimodes for the operator $H_\\varepsilon$, acting on $L^2(\\mathbb{R}^d)$, via restriction to the lattice $\\varepsilon\\mathbb{Z}^d$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-03T10:36:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37K60",
      "41A60"
    ],
    "keywords": [
      "difference operators",
      "asymptotic eigenfunctions",
      "construct formal asymptotic expansions",
      "one-well potential",
      "small parameter"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}