{
  "id": "2210.08462",
  "version": "v1",
  "published": "2022-10-16T06:34:44.000Z",
  "updated": "2022-10-16T06:34:44.000Z",
  "title": "Spectrality of Infinite Convolutions in $\\mathbb{R}^d$",
  "authors": [
    "Jun Jie Miao",
    "Zhiqiang Wang"
  ],
  "comment": "21 pages",
  "categories": [
    "math.CA",
    "math.FA"
  ],
  "abstract": "In this paper, we study the spectrality of infinite convolutions in $\\mathbb{R}^d$, where the spectrality means the corresponding square integrable function space admits a family of exponential functions as an orthonormal basis. Suppose that the infinite convolutions are generated by a sequence of admissible pairs in $\\mathbb{R}^d$. First, we give two sufficient conditions for their spectrality by using the equi-positive condition and the integral periodic zero set of measures. Then, we apply these results to a class of infinite convolutions supported in $[0,1]^d$, and we obtain the spectrality under a natural assumption. Finally, we relax the assumption and get a weaker sufficient condition in the $d$-dimensional space, where $d\\leq 3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-16T06:34:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C30",
      "28A80"
    ],
    "keywords": [
      "infinite convolutions",
      "spectrality",
      "square integrable function space admits",
      "integral periodic zero set",
      "corresponding square integrable function space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}