{
  "id": "1405.3682",
  "version": "v1",
  "published": "2014-05-14T20:53:05.000Z",
  "updated": "2014-05-14T20:53:05.000Z",
  "title": "Suffridge's convolution theorem for polynomials with zeros in the unit disk",
  "authors": [
    "Martin Lamprecht"
  ],
  "categories": [
    "math.CV",
    "math.CA"
  ],
  "abstract": "In 1976 Suffridge proved an intruiging theorem regarding the convolution of polynomials with zeros only on the unit circle. His result generalizes a special case of the fundamental Grace-Szeg\\\"o convolution theorem, but so far it is an open problem whether there is a Suffridge-like extension of the general Grace-Szeg\\\"o convolution theorem. In this paper we try to approach this question from two different directions: First, we show that Suffridge's convolution theorem holds for a certain class of polynomials with zeros in the unit disk and thus obtain an extension of one further special case of the Grace-Szeg\\\"o convolution theorem. Second, we present non-circular zero domains which stay invariant under the Grace-Szeg\\\"o convolution hoping that this will lead to further analogs of Suffridge's convolution theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-14T20:53:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30C10",
      "30C15"
    ],
    "keywords": [
      "unit disk",
      "polynomials",
      "special case",
      "suffridges convolution theorem holds",
      "non-circular zero domains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.3682L"
    }
  }
}