{
  "id": "0704.2268",
  "version": "v1",
  "published": "2007-04-18T15:04:13.000Z",
  "updated": "2007-04-18T15:04:13.000Z",
  "title": "Essential spectra of difference operators on $\\sZ^n$-periodic graphs",
  "authors": [
    "V. S. Rabinovich",
    "S. Roch"
  ],
  "doi": "10.1088/1751-8113/40/33/012",
  "categories": [
    "math-ph",
    "math.FA",
    "math.MP"
  ],
  "abstract": "Let $(\\cX, \\rho)$ be a discrete metric space. We suppose that the group $\\sZ^n$ acts freely on $X$ and that the number of orbits of $X$ with respect to this action is finite. Then we call $X$ a $\\sZ^n$-periodic discrete metric space. We examine the Fredholm property and essential spectra of band-dominated operators on $l^p(X)$ where $X$ is a $\\sZ^n$-periodic discrete metric space. Our approach is based on the theory of band-dominated operators on $\\sZ^n$ and their limit operators. In case $X$ is the set of vertices of a combinatorial graph, the graph structure defines a Schr\\\"{o}dinger operator on $l^p(X)$ in a natural way. We illustrate our approach by determining the essential spectra of Schr\\\"{o}dinger operators with slowly oscillating potential both on zig-zag and on hexagonal graphs, the latter being related to nano-structures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-04-18T15:04:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q10",
      "46N50",
      "47B36"
    ],
    "keywords": [
      "essential spectra",
      "difference operators",
      "periodic graphs",
      "periodic discrete metric space",
      "band-dominated operators"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2007,
      "month": "Aug",
      "volume": 40,
      "number": 33,
      "pages": 10109
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007JPhA...4010109R"
    }
  }
}