{
  "id": "1112.1746",
  "version": "v1",
  "published": "2011-12-08T01:36:46.000Z",
  "updated": "2011-12-08T01:36:46.000Z",
  "title": "Extended groups of semigroups and backward problems of heat equations",
  "authors": [
    "M. Arisawa"
  ],
  "comment": "Master's thesis",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "In this paper, we are concerned with backward solvabilities of heat equations, in an abstract framework. We show that semigroups $T_t$ in Banach spaces $X$, generated by heat operators, are extendable to groups in an extended space $E$, which is obtained by considering a sequence of wider Banach spaces containing $X$, i.e. $X$$/subset$$X_t$$/subset$$X_s$... $(t<s)$, under the following two conditions. One is the density assumption on a subset $D$ of $X$, the set of initial values $x$ from which $T_{-t}x$ exists for all $t>0$. Another is the backward uniqueness of the semigroup $T_t$. For example, we prove the holomorphic semigroup satisfies the above conditions, and thus is extendable to a group in a larger functional space $E$. We also studied structual properties of the extended space $E$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-12-08T01:36:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "heat equations",
      "extended groups",
      "backward problems",
      "semigroups",
      "wider banach spaces containing"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.1746A"
    }
  }
}