{
  "id": "math/0604294",
  "version": "v1",
  "published": "2006-04-12T18:20:27.000Z",
  "updated": "2006-04-12T18:20:27.000Z",
  "title": "Pseudodifferential Operators on Locally Compact Abelian Groups and Sjoestrand's Symbol Class",
  "authors": [
    "Karlheinz Grochenig",
    "Thomas Strohmer"
  ],
  "categories": [
    "math.FA",
    "math.AP"
  ],
  "abstract": "We investigate pseudodifferential operators on arbitrary locally compact abelian groups. As symbol classes for the Kohn-Nirenberg calculus we introduce a version of Sjoestrand's class. Pseudodifferential operators with such symbols form a Banach algebra that is closed under inversion. Since \"hard analysis\" techniques are not available on locally compact abelian groups, a new time-frequency approach is used with the emphasis on modulation spaces, Gabor frames, and Banach algebras of matrices. Sjoestrand's original results are thus understood as a phenomenon of abstract harmonic analysis rather than \"hard analysis\" and are proved in their natural context and generality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-04-12T18:20:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "pseudodifferential operators",
      "sjoestrands symbol class",
      "hard analysis",
      "banach algebra",
      "arbitrary locally compact abelian groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......4294G"
    }
  }
}