{
  "id": "2309.01313",
  "version": "v1",
  "published": "2023-09-04T02:02:05.000Z",
  "updated": "2023-09-04T02:02:05.000Z",
  "title": "$L^1\\rightarrow L^\\infty$ Dispersive estimates for Coulomb waves",
  "authors": [
    "Adam Black",
    "Ebru Toprak",
    "Bruno Vergara Biggio",
    "Jiahua Zou"
  ],
  "comment": "60 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We show the time decay of spherically symmetric Coulomb waves in $\\R^{3}$ for the case of a repulsive charge. By means of a distorted Fourier transform adapted to $H=-\\Delta+q\\cdot |x|^{-1}$, with $q>0$, we explicitly compute the kernel of the evolution operator $e^{itH}$. A detailed analysis of the kernel is then used to prove that for large times, $e^{i t H}$ obeys an $L^1 \\to L^\\infty$ dispersive estimate with the natural decay rate $t^{-\\f32}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-04T02:02:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q41",
      "35J10",
      "42B20",
      "33C15"
    ],
    "keywords": [
      "dispersive estimate",
      "spherically symmetric coulomb waves",
      "natural decay rate",
      "time decay",
      "evolution operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 60,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}