{
  "id": "2404.00585",
  "version": "v1",
  "published": "2024-03-31T07:05:49.000Z",
  "updated": "2024-03-31T07:05:49.000Z",
  "title": "Openness of the frame set on the hyperbolas",
  "authors": [
    "Aleksei Kulikov"
  ],
  "comment": "7 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We prove that for the functions of the form $g(x) = h(x) + \\frac{C}{x+i}$, where $h$ belongs to the continuous Wiener algebra $W_0$, the intersection of the frame set $\\mathcal{F}_g$ with every hyperbola $\\{\\alpha, \\beta > 0 \\mid \\alpha\\beta = c\\}$ is open in the relative topology. In particular, this applies to all rational functions $g$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-31T07:05:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "frame set",
      "rational functions",
      "continuous wiener algebra",
      "intersection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}