{
  "id": "2205.04106",
  "version": "v1",
  "published": "2022-05-09T08:17:21.000Z",
  "updated": "2022-05-09T08:17:21.000Z",
  "title": "Decay estimates for a class of wave equations on the Heisenberg group",
  "authors": [
    "Manli Song",
    "Jiale Yang"
  ],
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "In this paper, we study a class of dispersive wave equations on the Heisenberg group $H^n$. Based on the group Fourier transform on $H^n$, the properties of the Laguerre functions and the stationary phase lemma, we establish the decay estimates for a class of dispersive semigroup on $H^n$ given by $e^{it\\phi(\\mathcal{L})}$, where $\\phi: \\mathbb{R}^+ \\to \\mathbb{R}$ is smooth, and $\\mathcal{L}$ is the sub-Laplacian on $H^n$. Finally, using the duality arguments, we apply the obtained results to derive the Strichartz inequalities for the solutions of some specific equations, such as the fractional Schr\\\"{o}dinger equation, the fractional wave equation and the fourth-order Schr\\\"{o}dinger equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-09T08:17:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "heisenberg group",
      "decay estimates",
      "stationary phase lemma",
      "fractional wave equation",
      "group fourier transform"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}