{
  "id": "1404.1551",
  "version": "v1",
  "published": "2014-04-06T07:12:58.000Z",
  "updated": "2014-04-06T07:12:58.000Z",
  "title": "On the existence of orthogonal polynomials for oscillatory weights on a bounded interval",
  "authors": [
    "Hassan Majidian"
  ],
  "comment": "7 pages, 1 figure",
  "categories": [
    "math.NA"
  ],
  "abstract": "It is shown that the orthogonal polynomials, corresponding to the oscillatory weight $e^{\\im\\omega x}$, exists if $\\omega$ is a transcendental number and $\\tan\\omega/\\omega\\in\\Q$. Also, it is proved that such orthogonal polynomials exist for almost every $\\omega>0$, and the roots are all simple if $\\omega>0$ is either small enough or large enough.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-06T07:12:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65D32",
      "65R10"
    ],
    "keywords": [
      "orthogonal polynomials",
      "oscillatory weight",
      "bounded interval",
      "transcendental number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.1551M"
    }
  }
}