{
  "id": "1004.1429",
  "version": "v3",
  "published": "2010-04-08T21:35:25.000Z",
  "updated": "2011-11-24T21:45:53.000Z",
  "title": "Frames by Multiplication",
  "authors": [
    "Peter Balazs",
    "Carlos Cabrelli",
    "Sigrid Heineken",
    "Ursula Molter"
  ],
  "journal": "Current Development in Theory and Applications of Wavelets, Vol. 5 (2-3), pp. 165-186 (2011),",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this note we study frame-related properties of a sequence of functions multiplied by another function. In particular we study frame and Riesz basis properties. We apply these results to sets of irregular translates of a bandlimited function $h$ in $L^2(\\R^d)$. This is achieved by looking at a set of exponentials restricted to a set $E \\subset \\R^d$ with frequencies in a countable set $\\Lambda$ and multiplying it by the Fourier transform of a fixed function $h \\in L^2(E)$. Using density results due to Beurling, we prove the existence and give ways to construct frames by irregular translates.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-11-24T21:45:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multiplication",
      "irregular translates",
      "riesz basis properties",
      "fourier transform",
      "construct frames"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.1429B"
    }
  }
}