{
  "id": "2402.18367",
  "version": "v2",
  "published": "2024-02-28T14:39:39.000Z",
  "updated": "2024-03-15T11:06:43.000Z",
  "title": "Kernel theorems for operators on co-orbit spaces associated with localised frames",
  "authors": [
    "Dimitri Bytchenkoff",
    "Michael Speckbacher",
    "Peter Balazs"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Kernel theorems, in general, provide a convenient representation of bounded linear operators. For the operator acting on a concrete function space, this means that its action on any element of the space can be expressed as a generalised integral operator, in a way reminiscent of the matrix representation of linear operators acting on finite dimensional vector spaces. We prove kernel theorems for bounded linear operators acting on co-orbit spaces associated with localised frames. Our two main results consist in characterising the spaces of operators whose generalised integral kernels belong to the co-orbit spaces of test functions and distributions associated with the tensor product of the localised frames respectively. Moreover, using a version of Schur's test, we establish a characterisation of the bounded linear operators between some specific co-orbit spaces.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-03-15T11:06:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B35",
      "42C15",
      "46A32",
      "47B34"
    ],
    "keywords": [
      "kernel theorems",
      "localised frames",
      "bounded linear operators",
      "finite dimensional vector spaces",
      "linear operators acting"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}