{
  "id": "1311.1591",
  "version": "v2",
  "published": "2013-11-07T07:53:14.000Z",
  "updated": "2015-10-01T10:28:59.000Z",
  "title": "Stability for Time Dependent X-ray Transforms and Applications",
  "authors": [
    "Alden Waters"
  ],
  "comment": "this arxiv submission has been split into two separate submissions by separate authors, http://arxiv.org/abs/1406.4854 and the current version. the new version contains a extension to conformal factors",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove a logarithmic stability estimate for the time dependent X-ray transform on $\\mathbb{R}_t^+\\times\\mathbb{R}^n$. To do so, we extend a known result by Begmatov for the stability of the time dependent X-ray transform in $\\mathbb{R}^+_t\\times\\mathbb{R}^2$. We give some examples of stability and injectivity results in relationship to the Dirichlet-to-Neumann problem. In particular, under the Geometric Control Condtion, we derive inverse logarithmic stability estimates for time dependent conformal factors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-07T07:53:14.000Z",
      "title": "Global Stability for Time Dependent X-ray Transforms on Simple Manifolds and Applications",
      "abstract": "We prove a global stability estimate for the time-dependent X-ray transform on simple manifolds with dimension greater than or equal to $2$. We do this by extending a known result by Begmatov for stability of the time dependent X-ray transform in $\\mathbb{R}^+_t\\times\\mathbb{R}^2$. We give some examples of stability and injectivity results in relationship to the Dirichlet-to-Neumann problem.",
      "comment": null,
      "journal": null,
      "doi": null,
      "authors": [
        "Alden Waters",
        "Ricardo Salazar"
      ]
    },
    {
      "version": "v2",
      "updated": "2015-10-01T10:28:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R01",
      "35R30",
      "35L20",
      "58J45",
      "35A22"
    ],
    "keywords": [
      "time dependent x-ray transform",
      "simple manifolds",
      "applications",
      "global stability estimate",
      "time-dependent x-ray transform"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.1591W"
    }
  }
}