{
  "id": "1004.4087",
  "version": "v1",
  "published": "2010-04-23T10:09:49.000Z",
  "updated": "2010-04-23T10:09:49.000Z",
  "title": "Devinatz's moment problem: a description of all solutions",
  "authors": [
    "Sergey M. Zagorodnyuk"
  ],
  "comment": "26 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we study Devinatz's moment problem: to find a non-negative Borel measure $\\mu$ in a strip $\\Pi = \\{(x,\\phi):\\ x\\in \\mathbb{R},\\ -\\pi\\leq \\phi < \\pi\\},$ such that $\\int_\\Pi x^m e^{in\\phi} d\\mu = s_{m,n}$, $m\\in \\mathbb{Z}_+$, $n\\in \\mathbb{Z}$, where $\\{s_{m,n}\\}_{m\\in \\mathbb{Z}_+, n\\in \\mathbb{Z}}$ is a given sequence of complex numbers. We present a new proof of the Devinatz solvability criterion for this moment problem. We obtained a parameterization of all solutions of Devinatz's moment problem. We used an abstract operator approach and results of Godi\\v{c}, Lucenko and Shtraus.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-04-23T10:09:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "44A60"
    ],
    "keywords": [
      "description",
      "study devinatzs moment problem",
      "devinatz solvability criterion",
      "abstract operator approach",
      "complex numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.4087Z"
    }
  }
}