{
  "id": "1109.4367",
  "version": "v1",
  "published": "2011-09-20T17:19:54.000Z",
  "updated": "2011-09-20T17:19:54.000Z",
  "title": "New spectral multiplicities for ergodic actions",
  "authors": [
    "Anton V. Solomko"
  ],
  "comment": "17 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let G be a locally compact second countable Abelian group. Given a measure preserving action T of G on a standard probability space, let M(T) denote the set of essential values of the spectral multiplicity function of the Koopman unitary representation of G associated with T. In the case when G is either a discrete countable Abelian group or R^n, n>0, it is shown that the sets of the form {p,q,pq}, {p,q,r,pq,pr,qr,pqr} etc. or any multiplicative (and additive) subsemigroup of N are realizable as M(T) for a weakly mixing G-action T.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-09-20T17:19:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A15",
      "37A30"
    ],
    "keywords": [
      "ergodic actions",
      "compact second countable abelian group",
      "koopman unitary representation",
      "standard probability space",
      "discrete countable abelian group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.4367S"
    }
  }
}