{
  "id": "2305.16068",
  "version": "v1",
  "published": "2023-05-25T13:58:29.000Z",
  "updated": "2023-05-25T13:58:29.000Z",
  "title": "Optimal Polynomial Approximants in $H^p$",
  "authors": [
    "Raymond Centner",
    "Raymond Cheng",
    "Christopher Felder"
  ],
  "categories": [
    "math.FA",
    "math.CV"
  ],
  "abstract": "This work studies optimal polynomial approximants (OPAs) in the classical Hardy spaces on the unit disk, $H^p$ ($1 < p < \\infty$). In particular, we uncover some estimates concerning the OPAs of degree zero and one. It is also shown that if $f \\in H^p$ is an inner function, or if $p>2$ is an even integer, then the roots of the nontrivial OPA for $1/f$ are bounded from the origin by a distance depending only on $p$. For $p\\neq 2$, these results are made possible by the novel use of a family of inequalities which are derived from a Banach space analogue of the Pythagorean theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-25T13:58:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30E10",
      "46E30"
    ],
    "keywords": [
      "work studies optimal polynomial approximants",
      "banach space analogue",
      "hardy spaces",
      "unit disk",
      "pythagorean theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}