{
  "id": "1506.07162",
  "version": "v1",
  "published": "2015-06-23T19:57:09.000Z",
  "updated": "2015-06-23T19:57:09.000Z",
  "title": "On the density of polynomials under perturbations of the measure",
  "authors": [
    "Rafael del Rio",
    "Luis O. Silva"
  ],
  "comment": "12 pages, no figures",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We prove that if the polynomials are dense in $L_2(\\mathbb{R}, \\rho)$, then they are dense in $L_2(\\mathbb{R}, \\rho+\\mu)$ where $\\mu$ is a measure supported on a finite set of points. In particular, it will follow that $ \\rho+\\mu$ is a spectral measure of a Jacobi operator if $\\rho$ is. These results are obtained through the analysis of the Green functions of Jacobi operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-23T19:57:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A10",
      "47B36",
      "33E30"
    ],
    "keywords": [
      "polynomials",
      "jacobi operator",
      "perturbations",
      "finite set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150607162D"
    }
  }
}