{
  "id": "math/0605637",
  "version": "v1",
  "published": "2006-05-24T08:28:15.000Z",
  "updated": "2006-05-24T08:28:15.000Z",
  "title": "Equilibrium and eigenfunctions estimates in the semi-classical regime",
  "authors": [
    "Brice Camus"
  ],
  "comment": "13 pages, 1 figure, perhaps to be revised",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We establish eigenfunctions estimates, in the semi-classical regime, for critical energy levels associated to an isolated singularity. For Schr\\\"odinger operators, the asymptotic repartition of eigenvectors is the same as in the regular case, excepted in dimension 1 where a concentration at the critical point occurs. This principle extends to pseudo-differential operators and the limit measure is the Liouville measure as long as the singularity remains integrable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-05-24T08:28:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "semi-classical regime",
      "equilibrium",
      "critical energy levels",
      "singularity remains",
      "establish eigenfunctions estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}