{
  "id": "1710.10808",
  "version": "v1",
  "published": "2017-10-30T08:50:53.000Z",
  "updated": "2017-10-30T08:50:53.000Z",
  "title": "Constrained $L^2$-approximation by polynomials on subsets of the circle",
  "authors": [
    "L Baratchart",
    "Juliette Leblond",
    "Fabien Seyfert"
  ],
  "journal": "Mashreghi, Javad, Manolaki, Myrto, Gauthier, Paul M. New Trends in Approximation Theory. In Memory of Andr\\'e Boivin, 81, 2017, Fields Institute Communications",
  "categories": [
    "math.FA"
  ],
  "abstract": "We study best approximation to a given function, in the least square sense on a subset of the unit circle, by polynomials of given degree which are pointwise bounded on the complementary subset. We show that the solution to this problem, as the degree goes large, converges to the solution of a bounded extremal problem for analytic functions which is instrumental in system identification. We provide a numerical example on real data from a hyperfrequency filter.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-30T08:50:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "polynomials",
      "study best approximation",
      "square sense",
      "unit circle",
      "hyperfrequency filter"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}