{
  "id": "1612.03970",
  "version": "v1",
  "published": "2016-12-12T23:34:05.000Z",
  "updated": "2016-12-12T23:34:05.000Z",
  "title": "Singular values of weighted composition operators and second quantization",
  "authors": [
    "Mihai Putinar",
    "James E. Tener"
  ],
  "comment": "15 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We study a semigroup of weighted composition operators on the Hardy space of the disk $H^2(\\mathbb{D})$, and more generally on the Hardy space $H^2(U)$ attached to a simply connected domain $U$ with smooth boundary. Motivated by conformal field theory, we establish bounds on the singular values (approximation numbers) of these weighted composition operators. As a byproduct we obtain estimates on the singular values of the restriction operator (embedding operator) $H^2(V) \\to H^2(U)$ when $U \\subset V$ and the boundary of $U$ touches that of $V$. Moreover, using the connection between the weighted composition operators and restriction operators, we show that these operators exhibit an analog of the Fisher-Micchelli phenomenon for non-compact operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-12T23:34:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B33",
      "81T40",
      "30H10"
    ],
    "keywords": [
      "weighted composition operators",
      "singular values",
      "second quantization",
      "hardy space",
      "restriction operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}