{
  "id": "1012.3712",
  "version": "v2",
  "published": "2010-12-16T18:39:16.000Z",
  "updated": "2011-06-06T14:38:21.000Z",
  "title": "Darboux transformations of Jacobi matrices and Padé approximation",
  "authors": [
    "Maxim Derevyagin",
    "Vladimir Derkach"
  ],
  "comment": "28 pages (some typos are corrected)",
  "doi": "10.1016/j.laa.2011.05.035",
  "categories": [
    "math.CA",
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "Let J be a monic Jacobi matrix associated with the Cauchy transform F of a probability measure. We construct a pair of the lower and upper triangular block matrices L and U such that J=LU and the matrix J_c=UL is a monic generalized Jacobi matrix associated with the function F_c(z)=zF(z)+1. It turns out that the Christoffel transformation J_c of a bounded monic Jacobi matrix J can be unbounded. This phenomenon is shown to be related to the effect of accumulating at infinity of the poles of the Pad\\'e approximants of the function F_c although F_c is holomorphic at infinity. The case of the UL-factorization of J is considered as well.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-06-06T14:38:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B36",
      "30E05",
      "42C05"
    ],
    "keywords": [
      "darboux transformations",
      "jacobi matrices",
      "upper triangular block matrices",
      "approximation",
      "bounded monic jacobi matrix"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1012.3712D"
    }
  }
}