{
  "id": "2108.08093",
  "version": "v1",
  "published": "2021-08-18T11:29:10.000Z",
  "updated": "2021-08-18T11:29:10.000Z",
  "title": "Extreme points of the unit ball of Paley-Wiener space over two symmetric intervals",
  "authors": [
    "Alexander Ulanovskii",
    "Ilya Zlotnikov"
  ],
  "comment": "23 pages",
  "categories": [
    "math.FA",
    "math.CA",
    "math.CV"
  ],
  "abstract": "Let $PW_S^1$ be the space of integrable functions on $\\mathbb{R}$ whose Fourier transform vanishes outside $S$, where $S = [-\\sigma,-\\rho]\\cup[\\rho,\\sigma]$, $0<\\rho<\\sigma$. In the case $\\rho>\\sigma/2$, we present a complete description of the extreme points of the unit ball of $PW_S^1$. This description is no longer true if $\\rho<\\sigma/2$. For $\\rho>\\sigma/2$ we also show that every $f \\in PW^1_S, \\, \\|f\\|_1 =1,$ can be represented as $f = (f_1 + f_2)/2$ where $f_1$ and $f_2$ are extreme.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-18T11:29:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46A55",
      "30D20",
      "30D30"
    ],
    "keywords": [
      "unit ball",
      "extreme points",
      "paley-wiener space",
      "symmetric intervals",
      "fourier transform vanishes outside"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}