{
  "id": "1402.4641",
  "version": "v1",
  "published": "2014-02-19T12:32:57.000Z",
  "updated": "2014-02-19T12:32:57.000Z",
  "title": "Formal asymptotic expansion of the Faddeev-Green function in unbounded domains",
  "authors": [
    "G. N. Makrakis"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the Faddeev-Green function in the three-dimensional space and in a slab, and we construct formal asymptotic expansions for the large complex parameter appearing in this function. The basic idea of the construction is to express the Faddeev-Green function through the standard exponential integral and to use the standard asymptotic expansion of this special function. In the three-dimensional space, the constructed expansion of the Faddeev-Green function clearly suggests the form of the rigorous estimate proved by Sylvester and Uhlmann. and which is the basis of complex-geometric optics' techniques in inverse problems. A similar estimate is suggested for the slab case",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-19T12:32:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "faddeev-green function",
      "unbounded domains",
      "construct formal asymptotic expansions",
      "three-dimensional space",
      "standard asymptotic expansion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.4641M"
    }
  }
}