{
  "id": "math/0301060",
  "version": "v1",
  "published": "2003-01-07T22:21:50.000Z",
  "updated": "2003-01-07T22:21:50.000Z",
  "title": "Oscillation of Fourier Integrals with a spectral gap",
  "authors": [
    "A. Eremenko",
    "D. Novikov"
  ],
  "comment": "1 Figure",
  "categories": [
    "math.CA",
    "math.CV"
  ],
  "abstract": "Suppose that Fourier transform of a function f is zero on the interval [-a,a]. We prove that the lower density of sign changes of f is at least a/pi, provided that f is a locally integrable temperate distribution in the sense of Beurling, with non-quasianalytic weight. We construct an example showing that the last condition cannot be omitted.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-01-07T22:21:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42A38",
      "46F12",
      "46F20"
    ],
    "keywords": [
      "fourier integrals",
      "spectral gap",
      "oscillation",
      "non-quasianalytic weight",
      "fourier transform"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......1060E"
    }
  }
}