{
  "id": "2203.09069",
  "version": "v1",
  "published": "2022-03-17T03:54:12.000Z",
  "updated": "2022-03-17T03:54:12.000Z",
  "title": "A Rudin--de Leeuw type theorem for functions with spectral gaps",
  "authors": [
    "Konstantin M. Dyakonov"
  ],
  "comment": "8 pages; this is an abridged version of arXiv:2102.05857",
  "journal": "C. R. Math. Acad. Sci. Paris 359 (2021), 797--803",
  "doi": "10.5802/crmath.208",
  "categories": [
    "math.FA",
    "math.CA",
    "math.CV"
  ],
  "abstract": "Our starting point is a theorem of de Leeuw and Rudin that describes the extreme points of the unit ball in the Hardy space $H^1$. We extend this result to subspaces of $H^1$ formed by functions with smaller spectra. More precisely, given a finite set $\\mathcal K$ of positive integers, we prove a Rudin--de Leeuw type theorem for the unit ball of $H^1_{\\mathcal K}$, the space of functions $f\\in H^1$ whose Fourier coefficients $\\widehat f(k)$ vanish for all $k\\in\\mathcal K$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-17T03:54:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30H10",
      "30J10",
      "42A32",
      "46A55"
    ],
    "keywords": [
      "rudin-de leeuw type theorem",
      "spectral gaps",
      "unit ball",
      "finite set",
      "smaller spectra"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}