{
  "id": "0907.1172",
  "version": "v1",
  "published": "2009-07-07T09:35:11.000Z",
  "updated": "2009-07-07T09:35:11.000Z",
  "title": "Pontryagin Space Structure in Reproducing Kernel Hilbert Spaces over *-semigroups",
  "authors": [
    "Franciszek Hugon Szafraniec",
    "Michal Wojtylak"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "The geometry of spaces with indefinite inner product, known also as Krein spaces, is a basic tool for developing Operator Theory therein. In the present paper we establish a link between this geometry and the algebraic theory of *-semigroups. It goes via the positive definite functions and related to them reproducing kernel Hilbert spaces. Our concern is in describing properties of elements of the semigroup which determine shift operators which serve as Pontryagin fundamental symmetries",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-07-07T09:35:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A35",
      "46C20"
    ],
    "keywords": [
      "reproducing kernel hilbert spaces",
      "pontryagin space structure",
      "pontryagin fundamental symmetries",
      "determine shift operators",
      "indefinite inner product"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.1172H"
    }
  }
}