{
  "id": "1104.1827",
  "version": "v1",
  "published": "2011-04-11T01:49:28.000Z",
  "updated": "2011-04-11T01:49:28.000Z",
  "title": "Eberlein almost periodic functions that are not pseudo almost periodic",
  "authors": [
    "Bolis Basit",
    "Hans Günzler"
  ],
  "comment": "6 pages",
  "journal": "Monash University Analysis Paper 127, March 2011",
  "categories": [
    "math.FA"
  ],
  "abstract": "We construct Eberlein almost periodic functions $ f_j : J \\to H$ so that $||f_1(\\cdot)||$ is not ergodic and thus not Eberlein almost periodic and $||f_2(.)||$ is Eberlein almost periodic, but $f_1$ and $f_2$ are not pseudo almost periodic, the Parseval equation for them fails, where $J=\\r_+$ or $\\r$ and $H$ is a Hilbert space. This answers several questions posed by Zhang and Liu [18].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-04-11T01:49:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic functions",
      "hilbert space",
      "construct eberlein",
      "parseval equation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.1827B"
    }
  }
}