{
  "id": "1707.06166",
  "version": "v1",
  "published": "2017-07-19T15:48:08.000Z",
  "updated": "2017-07-19T15:48:08.000Z",
  "title": "Remarks on Inner Functions and Optimal Approximants",
  "authors": [
    "Catherine Bénéteau",
    "Matthew Fleeman",
    "Dmitry Khavinson",
    "Daniel Seco",
    "Alan Sola"
  ],
  "comment": "17 pages, submitted to the Canadian Math Bulletin",
  "categories": [
    "math.CA",
    "math.CV",
    "math.FA"
  ],
  "abstract": "We discuss the concept of inner function in reproducing kernel Hilbert spaces with an orthogonal basis of monomials and examine connections between inner functions and optimal polynomial approximants to $1/f$, where $f$ is a function in the space. We revisit some classical examples from this perspective, and show how a construction of Shapiro and Shields can be modified to produce inner functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-19T15:48:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E22",
      "30J05"
    ],
    "keywords": [
      "optimal approximants",
      "optimal polynomial approximants",
      "produce inner functions",
      "reproducing kernel hilbert spaces",
      "orthogonal basis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}