{
  "id": "1811.01083",
  "version": "v1",
  "published": "2018-11-02T20:47:25.000Z",
  "updated": "2018-11-02T20:47:25.000Z",
  "title": "Ordinary differential equations with point interactions: An inverse problem",
  "authors": [
    "Nuno Costa Dias",
    "Cristina Jorge",
    "Joao Nuno Prata"
  ],
  "comment": "23 pages, to appear in J. Math Anal. Appl",
  "doi": "10.1016/j.jmaa.2018.10.061",
  "categories": [
    "math.FA",
    "math.CA"
  ],
  "abstract": "Given a linear ordinary differential equation (ODE) on $\\RE$ and a set of interface conditions at a finite set of points $I \\subset \\RE$, we consider the problem of determining another differential equation whose {\\it global} solutions satisfy the original ODE on $\\RE \\backslash I $, and the interface conditions at $I $. Using an extension of the product of distributions with non-intersecting singular supports presented in [L. H\\\"ormander, The Analysis of Linear Partial Diffe\\-rential Operators I, Springer-Verlag, 1983], we determine an {\\it intrinsic} solution of this problem, i.e. a new ODE, satisfying the required conditions, and strictly defined within the space of Schwartz distributions. Using the same formalism, we determine a singular perturbation formulation for the $n$-th order derivative operator with interface conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-02T20:47:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inverse problem",
      "point interactions",
      "interface conditions",
      "linear ordinary differential equation",
      "th order derivative operator"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}