{
  "id": "2208.13756",
  "version": "v1",
  "published": "2022-08-29T17:45:26.000Z",
  "updated": "2022-08-29T17:45:26.000Z",
  "title": "Recovery of rapidly decaying source terms from dynamical samples in evolution equations",
  "authors": [
    "Akram Aldroubi",
    "Le Gong",
    "Ilya Krishtal"
  ],
  "categories": [
    "math.DS",
    "math.FA"
  ],
  "abstract": "We analyze the problem of recovering a source term of the form $h(t)=\\sum_{j}h_j\\phi(t-t_j)\\chi_{[t_j, \\infty)}(t)$ from space-time samples of the solution $u$ of an initial value problem in a Hilbert space of functions. In the expression of $h$, the terms $h_j$ belong to the Hilbert space, while $\\phi$ is a generic real-valued function with exponential decay at $\\infty$. The design of the sampling strategy takes into account noise in measurements and the existence of a background source.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-29T17:45:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46N99",
      "42C15",
      "94O20"
    ],
    "keywords": [
      "rapidly decaying source terms",
      "evolution equations",
      "dynamical samples",
      "hilbert space",
      "initial value problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}