{
  "id": "1303.7346",
  "version": "v1",
  "published": "2013-03-29T10:06:44.000Z",
  "updated": "2013-03-29T10:06:44.000Z",
  "title": "Sharp extensions for convoluted solutions of wave equations",
  "authors": [
    "Pedro J. Miana",
    "Verónica Poblete"
  ],
  "comment": "20 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we give sharp extensions of convoluted solutions of wave equations in abstract Banach spaces. The main technique is to use the algebraic structure, for convolution products $\\ast$ and $\\ast_c$, of these solutions which are defined by a version of the Duhamel's formula. We define algebra homomorphisms, for the convolution product $\\ast_c$, from a certain set of test-functions and apply our results to concrete examples of abstract wave equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-03-29T10:06:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47D09",
      "44A10",
      "44A35"
    ],
    "keywords": [
      "sharp extensions",
      "convoluted solutions",
      "convolution product",
      "define algebra homomorphisms",
      "abstract wave equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.7346M"
    }
  }
}