{
  "id": "1602.04750",
  "version": "v1",
  "published": "2016-02-15T17:57:54.000Z",
  "updated": "2016-02-15T17:57:54.000Z",
  "title": "Fourier bases and Fourier frames on self-affine measures",
  "authors": [
    "Dorin Ervin Dutkay",
    "Chun_Kit Lai",
    "Yang Wang"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "This paper gives a review of the recent progress in the study of Fourier bases and Fourier frames on self-affine measures. In particular, we emphasize the new matrix analysis approach for checking the completeness of a mutually orthogonal set. This method helps us settle down a long-standing conjecture that Hadamard triples generates self-affine spectral measures. It also gives us non-trivial examples of fractal measures with Fourier frames. Furthermore, a new avenue is open to investigate whether the Middle Third Cantor measure admits Fourier frames.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-15T17:57:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B05",
      "42A85",
      "28A25"
    ],
    "keywords": [
      "self-affine measures",
      "fourier bases",
      "measure admits fourier frames",
      "triples generates self-affine spectral",
      "generates self-affine spectral measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160204750E"
    }
  }
}