{
  "id": "1312.4772",
  "version": "v1",
  "published": "2013-12-17T13:25:16.000Z",
  "updated": "2013-12-17T13:25:16.000Z",
  "title": "Operators that coerce the surjectivity of convolution",
  "authors": [
    "Richard F. Bonner"
  ],
  "comment": "13 pages, no figures",
  "categories": [
    "math.FA"
  ],
  "abstract": "Considered are operators that leave the set of non-invertible (in the sense of Ehrenpreis) distributions stable. They simultaneously generalise the operation of convolution by a distribution with compact support and the operation of multiplication by a real analytic function; they are here called pseudo-convolutions since they also generalise pseudo-differential operators. (It is shown that the elliptic real analytic pseudo-differential operators leave both the non-invertible and the invertible distributions invariant.) But when the condition of real-analyticity is relaxed, such operators may map a non-invertible distribution to one invertible -- given that the invertibility in both cases concerns the same function space. By varying the space, however, one can measure the 'loss of non-invertibily' that a non-analytic perturbation may introduce. This phenomenon is here studied using the Beurling classes of functions and measuring the regularity of operator symbols in the Denjoy-Carleman sense; the Gevrey case turns out particularly simple.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-17T13:25:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convolution",
      "elliptic real analytic pseudo-differential operators",
      "real analytic pseudo-differential operators leave",
      "surjectivity",
      "distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.4772B"
    }
  }
}