{
  "id": "1612.01683",
  "version": "v1",
  "published": "2016-12-06T06:42:49.000Z",
  "updated": "2016-12-06T06:42:49.000Z",
  "title": "The propagation property and its application to inverse scattering for the fractional power of the negative Laplacian",
  "authors": [
    "Atsuhide Ishida"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Enss (1983) proved a propagation estimates for the usual free Schr\\\"odinger operator that turned out to be very useful for inverse scattering by Enss-Weder (1995). Since then, this method has been called the Enss-Weder time-dependent method. We study the same type of propagation estimate for the fractional power of the negative Laplacian and, as with the Enss-Weder method, we try to apply our estimate to inverse scattering. We find that the high velocity limit of the scattering operator uniquely determines the short-range interactions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-06T06:42:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inverse scattering",
      "fractional power",
      "negative laplacian",
      "propagation property",
      "application"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}