{
  "id": "1101.0502",
  "version": "v3",
  "published": "2011-01-03T12:03:10.000Z",
  "updated": "2012-04-20T01:20:11.000Z",
  "title": "Structure of wave operators in R^3",
  "authors": [
    "Marius Beceanu"
  ],
  "comment": "49 pages; final version, accepted for publication by AJM",
  "categories": [
    "math.AP",
    "math-ph",
    "math.FA",
    "math.MP"
  ],
  "abstract": "We prove a structure formula for the wave operators in R^3 and their adjoints for a scaling-invariant class of scalar potentials V, under the assumption that zero is neither an eigenvalue, nor a resonance for -\\Delta+V. The formula implies the boundedness of wave operators on L^p spaces, 1 \\leq p \\leq \\infty, on weighted L^p spaces, and on Sobolev spaces, as well as multilinear estimates for e^{itH} P_c. When V decreases rapidly at infinity, we obtain an asymptotic expansion of the wave operators. The first term of the expansion is of order < y >^{-4}, commutes with the Laplacian, and exists when V \\in <x >^{-3/2-\\epsilon} L^2. We also prove that the scattering operator S = W_-^* W_+ is an integrable combination of isometries. The proof is based on an abstract version of Wiener's theorem, applied in a new function space.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-04-20T01:20:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35P25",
      "35J10",
      "47A40",
      "47F05",
      "47N50",
      "81U40",
      "35C20"
    ],
    "keywords": [
      "wave operators",
      "asymptotic expansion",
      "scalar potentials",
      "formula implies",
      "sobolev spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.0502B"
    }
  }
}