{
  "id": "1207.2099",
  "version": "v3",
  "published": "2012-07-09T16:44:50.000Z",
  "updated": "2013-02-25T11:12:49.000Z",
  "title": "Schrödinger type propagators, pseudodifferential operators and modulation spaces",
  "authors": [
    "Elena Cordero",
    "Anita Tabacco",
    "Patrik Wahlberg"
  ],
  "comment": "25 pages, 2 figures, to appear in J. London Math. Soc",
  "doi": "10.1112/jlms/jdt020",
  "categories": [
    "math.FA",
    "math.AP"
  ],
  "abstract": "We prove continuity results for Fourier integral operators with symbols in modulation spaces, acting between modulation spaces. The phase functions belong to a class of nondegenerate generalized quadratic forms that includes Schr\\\"odinger propagators and pseudodifferential operators. As a byproduct we obtain a characterization of all exponents $p,q,r_1,r_2,t_1,t_2 \\in [1,\\infty]$ of modulation spaces such that a symbol in $M^{p,q}(\\mathbb R^{2d})$ gives a pseudodifferential operator that is continuous from $M^{r_1,r_2}(\\mathbb R^d)$ into $M^{t_1,t_2}(\\mathbb R^d)$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-02-25T11:12:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35S30",
      "35S05",
      "42B35"
    ],
    "keywords": [
      "modulation spaces",
      "schrödinger type propagators",
      "pseudodifferential operator",
      "fourier integral operators",
      "phase functions belong"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.2099C"
    }
  }
}