{
  "id": "1210.6326",
  "version": "v4",
  "published": "2012-10-23T18:44:04.000Z",
  "updated": "2015-08-28T12:33:40.000Z",
  "title": "A Spectral Multiplier Theorem associated with a Schrödinger Operator",
  "authors": [
    "Younghun Hong"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We establish a spectral multiplier theorem associated with a Schr\\\"odinger operator H=-\\Delta+V(x) in \\mathbb{R}^3. We present a new approach employing the Born series expansion for the resolvent. This approach provides an explicit integral representation for the difference between a spectral multiplier and a Fourier multiplier, and it allows us to treat a large class of Schr\\\"odinger operators without Gaussian heat kernel estimates. As an application to nonlinear PDEs, we show the local-in-time well-posedness of a 3d quintic nonlinear Schr\\\"odinger equation with a potential.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-12-26T22:02:44.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2015-08-28T12:33:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spectral multiplier theorem",
      "schrödinger operator",
      "gaussian heat kernel estimates",
      "3d quintic nonlinear",
      "explicit integral representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.6326H"
    }
  }
}