{
  "id": "1812.00386",
  "version": "v1",
  "published": "2018-12-02T13:08:18.000Z",
  "updated": "2018-12-02T13:08:18.000Z",
  "title": "g-frame representations with bounded operators",
  "authors": [
    "Yavar Khedmati",
    "Fatemeh Ghobadzadeh"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Dynamical sampling, as introduced by Aldroubi et al., deals with frame properties of sequences of the form $\\{T^i f_1\\}_{i\\in \\mathbb{N}}$, where $f_1$ belongs to Hilbert space $\\h$ and $T:\\h\\rightarrow\\h$ belongs to certain classes of the bounded operators. Christensen et al., study frames for $\\h$ with index set $\\mathbb{N}$ (or $\\mathbb{Z}$), that have representations in the form $\\{T^{i-1}f_1\\}_{i\\in \\mathbb{N}}$ (or $\\{T^if_0\\}_{i\\in \\mathbb{Z}}$). As frames of subspaces, fusion frames and generalized translation invariant systems are the spacial cases of $g$-frames, the purpose of this paper is to study $g$-frames $\\Lambda=\\{\\Lambda_i\\in B(\\h,\\K): i\\in I\\}$ $(I=\\mathbb{N}$ or $\\mathbb{Z}$) having the form $\\Lambda_{i+1}=\\Lambda_1 T^{i},$ for $T\\in B(\\h).$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-02T13:08:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A58",
      "42C15",
      "47A05"
    ],
    "keywords": [
      "bounded operators",
      "g-frame representations",
      "generalized translation invariant systems",
      "frame properties",
      "spacial cases"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}