{
  "id": "1609.05164",
  "version": "v1",
  "published": "2016-09-16T18:15:40.000Z",
  "updated": "2016-09-16T18:15:40.000Z",
  "title": "Dispersive estimates for Dirac Operators in dimension three with obstructions at threshold energies",
  "authors": [
    "Burak Erdogan",
    "William R. Green",
    "Ebru Toprak"
  ],
  "comment": "36 pages, submitted",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We investigate $L^1\\to L^\\infty$ dispersive estimates for the three dimensional Dirac equation with a potential. We also classify the structure of obstructions at the thresholds of the essential spectrum as being composed of a two dimensional space of resonances and finitely many eigenfunctions. We show that, as in the case of the Schr\\\"odinger evolution, the presence of a threshold obstruction generically leads to a loss of the natural $t^{-\\frac32}$ decay rate. In this case we show that the solution operator is composed of a finite rank operator that decays at the rate $t^{-\\frac12}$ plus a term that decays at the rate $t^{-\\frac32}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-16T18:15:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dispersive estimates",
      "threshold energies",
      "dirac operators",
      "dimensional dirac equation",
      "finite rank operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}