{
  "id": "1708.04759",
  "version": "v1",
  "published": "2017-08-16T03:35:58.000Z",
  "updated": "2017-08-16T03:35:58.000Z",
  "title": "A Nonlinear Plancherel Theorem with Applications to Global Well-Posedness for the Defocusing Davewy-Stewartson Equation and to the Inverse Boundary Value Problem of Calderon",
  "authors": [
    "Adrian I. Nachman",
    "Idan Regev",
    "Daniel I. Tataru"
  ],
  "comment": "38 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove a Plancherel theorem for a nonlinear Fourier transform in two dimensions arising in the Inverse-Scattering method for the defocusing Davey-Stewartson II equation. We then use it to prove global well-posedness and scattering in $L^2$ for defocusing DSII. This Plancherel theorem also implies global uniqueness in the inverse boundary value problem of Calder\\'on in dimension $2$, for conductivities $\\sigma>0$ with $\\log \\sigma \\in \\dot H^1$. The proof of the nonlinear Plancherel theorem includes new estimates on fractional integrals in Sobolev spaces, as well as a new result on $L^2$- boundedness of pseudo-differential equations with non-smooth symbols, valid in all dimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-16T03:35:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inverse boundary value problem",
      "nonlinear plancherel theorem",
      "defocusing davewy-stewartson equation",
      "global well-posedness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}