{
  "id": "1902.03413",
  "version": "v1",
  "published": "2019-02-09T11:53:13.000Z",
  "updated": "2019-02-09T11:53:13.000Z",
  "title": "Decay and Smoothness for Eigenfunctions of Localization Operators",
  "authors": [
    "Federico Bastianoni",
    "Elena Cordero",
    "Fabio Nicola"
  ],
  "comment": "21 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We study decay and smoothness properties for eigenfunctions of localization operators. Considering symbols in the wide modulation space M^{p,\\infty}(R^{2d}) (containing the Lebesgue space L^p(R^{2d})), p < \\infty, and two general windows in the Schwartz class S(R^d), we show that L^2-eigenfuctions with non-zero eigenvalue are indeed highly compressed onto a few Gabor atoms. Similarly, for symbols in the weighted modulation space M^\\infty_{v_s\\otimes 1}(R^{2d}), s > 0, the corresponding L^2-eigenfunctions are actually in S(R^d). An important role is played by quasi-Banach Wiener amalgam and modulation spaces. As a tool, new convolution relations for modulation spaces and multiplication relations for Wiener amalgam spaces in the quasi-Banach setting are exhibited.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-09T11:53:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47G30",
      "35S05",
      "46E35",
      "47B10"
    ],
    "keywords": [
      "localization operators",
      "eigenfunctions",
      "quasi-banach wiener amalgam",
      "wiener amalgam spaces",
      "wide modulation space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}