{
  "id": "math/0502283",
  "version": "v1",
  "published": "2005-02-14T10:58:54.000Z",
  "updated": "2005-02-14T10:58:54.000Z",
  "title": "Pseudo-differential operators in algebras of generalized functions and global hypoellipticity",
  "authors": [
    "Claudia Garetto"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "The aim of this work is to develop a global calculus for pseudo-differential operators acting on suitable algebras of generalized functions. In particular, a condition of global hypoellipticity of the symbols gives a result of regularity for the corresponding pseudo-differential equations. This calculus and this frame are proposed as tools for the study in Colombeau algebras of partial differential equations globally defined on $\\mathbb{R}^n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-02-14T10:58:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46F30",
      "47G30",
      "35H05"
    ],
    "keywords": [
      "pseudo-differential operators",
      "global hypoellipticity",
      "generalized functions",
      "colombeau algebras",
      "partial differential equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......2283G"
    }
  }
}