{
  "id": "1601.03183",
  "version": "v1",
  "published": "2016-01-13T09:45:10.000Z",
  "updated": "2016-01-13T09:45:10.000Z",
  "title": "The essential spectrum of the Neumann--Poincaré operator on a domain with corners",
  "authors": [
    "Karl-Mikael Perfekt",
    "Mihai Putinar"
  ],
  "categories": [
    "math.FA",
    "math.SP"
  ],
  "abstract": "Exploiting the homogeneous structure of a wedge in the complex plane, we compute the spectrum of the anti-linear Ahlfors--Beurling transform acting on the Bergman space of the wedge. A classical similarity equivalence between the Ahlfors--Beurling transform and the Neumann--Poincar\\'e operator then characterizes the spectrum also of the latter on a wedge. A localization technique leads to a complete description of the essential spectrum of the Neumann--Poincar\\'e operator on a planar domain with corners.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-13T09:45:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "essential spectrum",
      "neumann-poincare operator",
      "complete description",
      "complex plane",
      "classical similarity equivalence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160103183P"
    }
  }
}