{
  "id": "1312.7739",
  "version": "v1",
  "published": "2013-12-30T15:30:25.000Z",
  "updated": "2013-12-30T15:30:25.000Z",
  "title": "Cyclicity in reproducing kernel Hilbert spaces of analytic functions",
  "authors": [
    "Emmanuel Fricain",
    "Javad Mashreghi",
    "Daniel Seco"
  ],
  "comment": "16 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "We introduce a large family of reproducing kernel Hilbert spaces $\\mathcal{H} \\subset \\mbox{Hol}(\\mathbb{D})$, which include the classical Dirichlet-type spaces $\\mathcal{D}_\\alpha$, by requiring normalized monomials to form a Riesz basis for $\\mathcal{H}$. Then, after precisely evaluating the $n$-th optimal norm and the $n$-th approximant of $f(z)=1-z$, we completely characterize the cyclicity of functions in $\\mbox{Hol}(\\overline{\\mathbb{D}})$ with respect to the forward shift.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-30T15:30:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A16",
      "47B32",
      "47B37"
    ],
    "keywords": [
      "reproducing kernel hilbert spaces",
      "analytic functions",
      "th optimal norm",
      "classical dirichlet-type spaces",
      "th approximant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.7739F"
    }
  }
}