{
  "id": "0802.0565",
  "version": "v1",
  "published": "2008-02-05T08:54:16.000Z",
  "updated": "2008-02-05T08:54:16.000Z",
  "title": "Criteria for Bochner's extension problem",
  "authors": [
    "Michael Ruzhansky",
    "Mitsuru Sugimoto"
  ],
  "comment": "12 pages",
  "journal": "Asymptotic Analysis, 66 (2010), 125-138",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "A necessary and sufficient condition for the resolution of the weak extension problem is given. This criterion is applied to also give a criterion for the solvability of the classical Bochner's extension problem in the $L^p$-category. The solution of the $L^p$-extension problem by Bochner giving the relation between the order of the operator, the dimension, and index $p$, for which the $L^p$-extension property holds, can be viewed as a subcritical case of the general $L^p$-extension problem. In general, this property fails in some critical and in all supercritical cases. In this paper, the $L^p$-extension problem is investigated for operators of all orders and for all $1\\leq p\\leq\\infty$. Necessary and sufficient conditions on the subset of $L^p$ are given for which the $L^p$-extension property still holds, in the critical and supercritical cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-02-05T08:54:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B60",
      "35D10"
    ],
    "keywords": [
      "sufficient condition",
      "supercritical cases",
      "weak extension problem",
      "classical bochners extension problem",
      "extension property holds"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0802.0565R"
    }
  }
}