{
  "id": "2103.12267",
  "version": "v1",
  "published": "2021-03-23T02:26:53.000Z",
  "updated": "2021-03-23T02:26:53.000Z",
  "title": "Continuous frames in Krein spaces",
  "authors": [
    "Diego Carrillo",
    "Kevin Esmeral",
    "Elmar Wagner"
  ],
  "comment": "19 pages, continuation of arXiv:1304.2450",
  "categories": [
    "math.FA"
  ],
  "abstract": "The purpose of this paper is to propose a definition of continuous frames of rank n for Krein spaces and to study their basic properties. Similarly to the Hilbert space case, continuous frames are characterized by the analysis, the pre-frame and the frame operator, where the latter gives rise to a frame decomposition theorem. The paper includes a discussion of similar, dual and Parseval frames and of reproducing kernels. In addition, the importance of the fundamental symmetry in the formula for the frame operator in a Krein space is clarified. As prime examples, it is shown how to transfer continuous frames for Hilbert spaces to Krein spaces arising from a possibly non-regular Gram operator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-23T02:26:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C15",
      "46B15",
      "46C05"
    ],
    "keywords": [
      "krein space",
      "frame operator",
      "hilbert space case",
      "possibly non-regular gram operator",
      "frame decomposition theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}