{
  "id": "2201.10230",
  "version": "v1",
  "published": "2022-01-25T10:40:09.000Z",
  "updated": "2022-01-25T10:40:09.000Z",
  "title": "Toeplitz and related operators on polyanalytic Fock spaces",
  "authors": [
    "Raffael Hagger"
  ],
  "comment": "20 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We give a characterization of compact and Fredholm operators on polyanalytic Fock spaces in terms of limit operators. As an application we obtain a generalization of the Bauer-Isralowitz theorem using a matrix valued Berezin type transform. We then apply this theorem to Toeplitz and Hankel operators to obtain necessary and sufficient conditions for compactness. As it turns out, whether or not a Toeplitz or Hankel operator is compact does not depend on the polyanalytic order. For Hankel operators this even holds on the true polyanalytic Fock spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-01-25T10:40:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B35",
      "30H20",
      "47B07",
      "47A53",
      "47L80"
    ],
    "keywords": [
      "related operators",
      "hankel operator",
      "true polyanalytic fock spaces",
      "matrix valued berezin type transform",
      "bauer-isralowitz theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}