{
  "id": "math/0412536",
  "version": "v1",
  "published": "2004-12-30T02:17:19.000Z",
  "updated": "2004-12-30T02:17:19.000Z",
  "title": "Sharp upper bounds on the number of the scattering poles",
  "authors": [
    "Plamen Stefanov"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "For various compactly supported perturbations of the Laplacian in odd dimensions $n$, we prove a sharp upper bound of the resonance counting function $N(r)$ of the type $N(r) \\le A_n r^n(1+o(1))$ with an explicit constant $A_n$. In a few special cases, we show that this estimate turns into an asymptotic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-12-30T02:17:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35P25"
    ],
    "keywords": [
      "sharp upper bound",
      "scattering poles",
      "odd dimensions",
      "resonance counting function",
      "explicit constant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}