{
  "id": "1705.03759",
  "version": "v1",
  "published": "2017-05-06T11:39:35.000Z",
  "updated": "2017-05-06T11:39:35.000Z",
  "title": "Extension of Vietoris' inequalities for positivity of trigonometric polynomials",
  "authors": [
    "Priyanka Sangal",
    "A. Swaminathan"
  ],
  "comment": "17 PAGES",
  "categories": [
    "math.CA",
    "math.CV"
  ],
  "abstract": "In this work, conditions on the coefficients $\\{a_k\\}$ are considered so that the corresponding sine sum $\\displaystyle\\sum_{k=1}^{n}a_k \\sin{k\\theta}$ and cosine sum $a_0+\\displaystyle\\sum_{k=1}^n a_k \\cos{k\\theta}$ are positive in the unit disc $\\mathbb{D}$. The monotonicity property of cosine sums is also discussed. Further a generalization of renowned Theorem of Vietoris' for the positivity of cosine and sine sums is established. Various new results which follow from these inequalities include improved estimates for the location of the zeros of a class of trigonometric polynomials and new positive sums for Gegenbauer polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-06T11:39:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42A05"
    ],
    "keywords": [
      "trigonometric polynomials",
      "positivity",
      "inequalities",
      "cosine sum",
      "corresponding sine sum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}