{
  "id": "1802.10314",
  "version": "v1",
  "published": "2018-02-28T09:05:16.000Z",
  "updated": "2018-02-28T09:05:16.000Z",
  "title": "Almost diagonalization of $τ$-pseudodifferential operators with symbols in Wiener amalgam and modulation spaces",
  "authors": [
    "Elena Cordero",
    "Fabio Nicola",
    "Salvatore Ivan Trapasso"
  ],
  "comment": "29 pages, submitted",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we focus on the almost-diagonalization properties of $\\tau$-pseudodifferential operators using techniques from time-frequency analysis. Our function spaces are modulation spaces and the special class of Wiener amalgam spaces arising by considering the action of the Fourier transform of modulation spaces. A particular example is provided by the Sj\\\"ostrand class, for which Gr\\\"ochenig exhibited the almost diagonalization of Weyl operators. We shall show that such result can be extended to any $\\tau$-pseudodifferential operator, for $\\tau \\in [0,1]$, also with symbol in weighted Wiener amalgam spaces. As a consequence, we infer boundedness, algebra and Wiener properties for $\\tau$-pseudodifferential operators on Wiener amalgam and modulation spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-28T09:05:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "modulation spaces",
      "pseudodifferential operator",
      "weighted wiener amalgam spaces",
      "wiener properties",
      "time-frequency analysis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}