{
  "id": "2207.09802",
  "version": "v1",
  "published": "2022-07-20T10:32:21.000Z",
  "updated": "2022-07-20T10:32:21.000Z",
  "title": "Sturm-Liouville systems on a class of Hilbert spaces",
  "authors": [
    "Anthony Hastir",
    "Judicaël Mohet",
    "Joseph J. Winkin"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "The class of Sturm-Liouville operators on the space of square integrable functions on a finite interval is considered. According to the Riesz-spectral property, the self-adjointness and the positivity of such unbounded linear operators on that space, a class of Hilbert spaces constructed as the domains of the positive (in particular, fractional) powers of any Sturm-Liouville operator is considered. On these spaces, it is shown that any Sturm-Liouville operator is a Riesz-spectral operator that possesses the same eigenvalues as the original ones, associated to rescaled eigenfunctions. This constitutes the central result of this note. Properties related to the C_0-semigroup generated by the opposite of such Riesz-spectral operator are also highlighted. The main result is applied on a diffusion-convection-reaction system in order notably to show that the dynamics operator is the infinitesimal generator of a compact C_0-semigroup on some Sobolev space of integer order. The advantage of performing such an approach is illustrated on this example by means of an observability analysis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-20T10:32:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hilbert spaces",
      "sturm-liouville systems",
      "sturm-liouville operator",
      "riesz-spectral operator",
      "central result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}