{
  "id": "1905.10122",
  "version": "v1",
  "published": "2019-05-24T10:11:45.000Z",
  "updated": "2019-05-24T10:11:45.000Z",
  "title": "A Subnormal Completion Problem for Weighted Shifts on Directed Trees, II",
  "authors": [
    "George R. Exner",
    "Il Bong Jung",
    "Jan Stochel",
    "Hye Yeong Yun"
  ],
  "comment": "19 pages, 4 figures",
  "categories": [
    "math.FA"
  ],
  "abstract": "The subnormal completion problem on a directed tree is to determine, given a collection of weights on a subtree, whether the weights may be completed to the weights of a subnormal weighted shift on the directed tree. We study this problem on a directed tree with a single branching point, $\\eta$ branches and the trunk of length $1$ and its subtree which is the \"truncation\" of the full tree to vertices of generation not exceeding $2$. We provide necessary and sufficient conditions written in terms of two parameter sequences for the existence of a subnormal completion in which the resulting measures are $2$-atomic. As a consequence, we obtain a solution of the subnormal completion problem for this pair of directed trees when $\\eta < \\infty$. If $\\eta=2$, we present a solution written explicitly in terms of initial data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-24T10:11:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B20",
      "47B37",
      "05C20"
    ],
    "keywords": [
      "subnormal completion problem",
      "directed tree",
      "sufficient conditions written",
      "subnormal weighted shift",
      "initial data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}