{
  "id": "2112.08680",
  "version": "v1",
  "published": "2021-12-16T07:56:35.000Z",
  "updated": "2021-12-16T07:56:35.000Z",
  "title": "Completeness of Discrete Translates in $H^1(\\mathbb{R})$",
  "authors": [
    "Bhawna Dharra",
    "S. Sivananthan"
  ],
  "journal": "Proceedings of the American Mathematical Society, 150, Pages 5281-5291, 2022",
  "doi": "10.1090/proc/16070",
  "categories": [
    "math.FA"
  ],
  "abstract": "We provide a characterization of discrete sets $\\Lambda \\subset \\mathbb{R}$ that admit a function whose $\\Lambda$-translates are complete in the Hardy space $H^1(\\mathbb{R})$. In particular, we show that such a set cannot be uniformly discrete. We then give a uniformly discrete $\\Lambda \\subset \\mathbb{R}$ which admits a pair of functions such that their $\\Lambda$-translates are complete in $H^1(\\mathbb{R})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-12-16T07:56:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B30",
      "42C30",
      "42A65"
    ],
    "keywords": [
      "discrete translates",
      "completeness",
      "uniformly discrete"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}