{
  "id": "2401.15450",
  "version": "v1",
  "published": "2024-01-27T16:20:17.000Z",
  "updated": "2024-01-27T16:20:17.000Z",
  "title": "Characterization of frames for source recovery from dynamical samples",
  "authors": [
    "Akram Aldroubi",
    "Rocio Diaz Martin",
    "Le Gong",
    "Javad Mashreghi",
    "Ivan Medri"
  ],
  "categories": [
    "math.DS",
    "math.FA"
  ],
  "abstract": "In this paper, we address the problem of recovering constant source terms in a discrete dynamical system represented by $x_{n+1} = Ax_n + w$, where $x_n$ is the $n$-th state in a Hilbert space $\\mathcal{H}$, $A$ is a bounded linear operator in $\\mathcal{B}(\\mathcal{H})$, and $w$ is a source term within a closed subspace $W$ of $\\HH$. Our focus is on the stable recovery of $w$ using time-space sample measurements formed by inner products with vectors from a Bessel system $\\mathcal{G} \\subset \\mathcal{H}$. We establish the necessary and sufficient conditions for the recovery of $w$ from these measurements, independent of the unknown initial state $x_0$ and for any $w \\in W$. This research is particularly relevant to applications such as environmental monitoring, where precise source identification is critical.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-27T16:20:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "source recovery",
      "dynamical samples",
      "characterization",
      "time-space sample measurements",
      "recovering constant source terms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}