{
  "id": "math-ph/0703077",
  "version": "v2",
  "published": "2007-03-27T14:58:41.000Z",
  "updated": "2007-04-26T16:05:33.000Z",
  "title": "p-Adic Schrödinger-Type Operator with Point Interactions",
  "authors": [
    "S. Albeverio",
    "S. Kuzhel",
    "S. Torba"
  ],
  "journal": "J. Math. Anal. Appl. 338 (2008), No. 2, 1267-1281",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "A $p$-adic Schr\\\"{o}dinger-type operator $D^{\\alpha}+V_Y$ is studied. $D^{\\alpha}$ ($\\alpha>0$) is the operator of fractional differentiation and $V_Y=\\sum_{i,j=1}^nb_{ij}<\\delta_{x_j}, \\cdot>\\delta_{x_i}$ $(b_{ij}\\in\\mathbb{C})$ is a singular potential containing the Dirac delta functions $\\delta_{x}$ concentrated on points $\\{x_1,...,x_n\\}$ of the field of $p$-adic numbers $\\mathbb{Q}_p$. It is shown that such a problem is well-posed for $\\alpha>1/2$ and the singular perturbation $V_Y$ is form-bounded for $\\alpha>1$. In the latter case, the spectral analysis of $\\eta$-self-adjoint operator realizations of $D^{\\alpha}+V_Y$ in $L_2(\\mathbb{Q}_p)$ is carried out.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-04-26T16:05:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A10",
      "47A55",
      "81Q10"
    ],
    "keywords": [
      "p-adic schrödinger-type operator",
      "point interactions",
      "self-adjoint operator realizations",
      "dirac delta functions",
      "adic numbers"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.jmaa.2007.06.016",
      "journal": "Journal of Mathematical Analysis and Applications",
      "year": 2008,
      "month": "Feb",
      "volume": 338,
      "number": 2,
      "pages": 1267
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008JMAA..338.1267A"
    }
  }
}