{
  "id": "2011.06162",
  "version": "v1",
  "published": "2020-11-12T02:04:06.000Z",
  "updated": "2020-11-12T02:04:06.000Z",
  "title": "$L^2$ boundedness of pseudodifferential operators on manifolds with ends",
  "authors": [
    "Shota Fukushima"
  ],
  "comment": "29 pages",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "We investigate properties of pseudodifferential operators on $L^2$ space on manifold with ends including asymptotically conical or hyperbolic ends. Our pseudodifferential operators are a generalization of the canonical quantization which naturally appears in the quantum mechanics on curved spaces. We prove a Calder\\'on-Vaillancourt type theorem for our pseudodifferential operators and discuss a construction of parametrix of elliptic differential operators on manifolds with ends.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-12T02:04:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "pseudodifferential operators",
      "boundedness",
      "elliptic differential operators",
      "calderon-vaillancourt type theorem",
      "hyperbolic ends"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}