{
  "id": "math/0604087",
  "version": "v1",
  "published": "2006-04-04T22:04:03.000Z",
  "updated": "2006-04-04T22:04:03.000Z",
  "title": "Harmonic Analysis of Fractal Measures",
  "authors": [
    "Palle E. T. Jorgensen",
    "Steen Pedersen"
  ],
  "comment": "38 pages, AMS-TeX (\"amsppt\" document style)",
  "journal": "Constr. Approx. 12 (1996), 1--30",
  "categories": [
    "math.FA"
  ],
  "abstract": "This paper introduces Fourier duality for a class of affine iterated function systems (IFS) T_i. These systems are determined by a finite family of contractive affine maps in R^d. Our Fourier duality applies to the resulting probability measure mu which is fixed by (T_i). When the IFS is given, the support of the associated mu is a compact set X in R^d, typically a fractal. Our Fourier duality refers to the Hilbert space L^2(X, mu): We show that under a certain unitarity condition involving a pair of affine iterated function systems (T_i) and (S_j) it is possible to recursively construct a Fourier bases in the Hilbert space L^2(X, mu) with the Fourier basis for one depending on the other.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-04-04T22:04:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A75",
      "42B10",
      "46L55",
      "05B45"
    ],
    "keywords": [
      "fractal measures",
      "harmonic analysis",
      "affine iterated function systems",
      "hilbert space",
      "fourier duality applies"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "AMS-TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......4087J"
    }
  }
}