{
  "id": "2206.07342",
  "version": "v1",
  "published": "2022-06-15T07:55:13.000Z",
  "updated": "2022-06-15T07:55:13.000Z",
  "title": "Spectrality of Infinite Convolutions and Random Convolutions",
  "authors": [
    "Wenxia Li",
    "Jun Jie Miao",
    "Zhiqiang Wang"
  ],
  "comment": "29 pages",
  "categories": [
    "math.CA",
    "math.FA"
  ],
  "abstract": "In this paper, we study spectral measures whose square integrable spaces admit a family of exponential functions as an orthonormal basis. First, we characterize the spectrality of infinite convolutions generated by a sequence of admissible pairs. Next, we show that given finitely many admissible pairs, almost all random convolutions are spectral measures. Moreover, we give a complete characterization of spectrality of random convolutions for some special cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-15T07:55:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C30",
      "28A80"
    ],
    "keywords": [
      "random convolutions",
      "infinite convolutions",
      "spectrality",
      "study spectral measures",
      "square integrable spaces admit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}