{
  "id": "1608.03473",
  "version": "v1",
  "published": "2016-08-11T14:17:00.000Z",
  "updated": "2016-08-11T14:17:00.000Z",
  "title": "Discrete Analogue of Generalized Hardy Spaces and Multiplication Operators on Homogenous Trees",
  "authors": [
    "Perumal Muthukumar",
    "Saminathan Ponnusamy"
  ],
  "comment": "16 pages",
  "journal": "A version of it is available online in Analysis and Mathematical Physics, 2016",
  "doi": "10.1007/s13324-016-0141-9",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this article, we define discrete analogue of generalized Hardy spaces and its separable subspace on a homogenous rooted tree and study some of its properties such as completeness, inclusion relations with other spaces, separability, growth estimate for functions in these spaces and their consequences. Equivalent conditions for multiplication operators to be bounded and compact are also obtained. Furthermore, we discuss about point spectrum, approximate point spectrum and spectrum of multiplication operators and discuss when a multiplication operator is an isometry.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-11T14:17:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B38",
      "05C05",
      "46B50",
      "46B26"
    ],
    "keywords": [
      "generalized hardy spaces",
      "multiplication operator",
      "homogenous trees",
      "define discrete analogue",
      "approximate point spectrum"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}