{
  "id": "1104.5264",
  "version": "v2",
  "published": "2011-04-27T22:46:12.000Z",
  "updated": "2013-05-10T11:37:06.000Z",
  "title": "On the many Dirichlet Laplacians on a non-convex polygon and their approximations by point interactions",
  "authors": [
    "Andrea Posilicano"
  ],
  "comment": "Slightly revised version. Accepted for publication in Journal of Functional Analysis",
  "doi": "10.1016/j.jfa.2013.05.013",
  "categories": [
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "By Birman and Skvortsov it is known that if $\\Omegasf$ is a planar curvilinear polygon with $n$ non-convex corners then the Laplace operator with domain $H^2(\\Omegasf)\\cap H^1_0(\\Omegasf)$ is a closed symmetric operator with deficiency indices $(n,n)$. Here we provide a Kre\\u\\i n-type resolvent formula for any self-adjoint extensions of such an operator, i.e. for the set of self-adjoint non-Friedrichs Dirichlet Laplacians on $\\Omegasf$, and show that any element in this set is the norm resolvent limit of a suitable sequence of Friedrichs-Dirichlet Laplacians with $n$ point interactions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-05-10T11:37:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "point interactions",
      "non-convex polygon",
      "self-adjoint non-friedrichs dirichlet laplacians",
      "approximations",
      "norm resolvent limit"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.5264P"
    }
  }
}