{
  "id": "1309.4322",
  "version": "v1",
  "published": "2013-09-17T14:22:44.000Z",
  "updated": "2013-09-17T14:22:44.000Z",
  "title": "Generators with a closure relation",
  "authors": [
    "Felix Schwenninger",
    "Hans Zwart"
  ],
  "comment": "9 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Assume that a block operator of the form $\\left(\\begin{smallmatrix}A_{1}\\\\A_{2}\\quad 0\\end{smallmatrix}\\right)$, acting on the Banach space $X_{1}\\times X_{2}$, generates a contraction $C_{0}$-semigroup. We show that the operator $A_{S}$ defined by $A_{S}x=A_{1}\\left(\\begin{smallmatrix}x\\\\SA_{2}x\\end{smallmatrix}\\right)$ with the natural domain generates a contraction semigroup on $X_{1}$. Here, $S$ is a boundedly invertible operator for which $\\epsilon\\ide-S^{-1}$ is dissipative for some $\\epsilon>0$. With this result the existence and uniqueness of solutions of the heat equation can be derived from the wave equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-17T14:22:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47D06",
      "47B44",
      "34G10"
    ],
    "keywords": [
      "closure relation",
      "generators",
      "natural domain generates",
      "block operator",
      "wave equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.4322S"
    }
  }
}