{
  "id": "2203.01499",
  "version": "v1",
  "published": "2022-03-03T03:21:42.000Z",
  "updated": "2022-03-03T03:21:42.000Z",
  "title": "Smoothness of the fundamental solution of Schrödinger equations with mild trapping",
  "authors": [
    "Kouichi Taira"
  ],
  "comment": "6 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this short note, smoothness of the fundamental solution of Schr\\\"odinger equations on a complete manifold is studied. It is shown that (1) the fundamental solution is smooth under \"mild\" trapping conditions; (2) there is a Riemannian manifold which is equal to Euclidean space outside a compact set such that the fundamental solution is not smooth.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-03T03:21:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A08",
      "35A21",
      "35R01"
    ],
    "keywords": [
      "fundamental solution",
      "schrödinger equations",
      "mild trapping",
      "smoothness",
      "euclidean space outside"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}