{
  "id": "2311.16747",
  "version": "v1",
  "published": "2023-11-28T12:44:25.000Z",
  "updated": "2023-11-28T12:44:25.000Z",
  "title": "A Note on the Completeness of All Translates of a Function in the Orlicz Spaces",
  "authors": [
    "Bhawna Dharra",
    "S. Sivananthan"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We give a characterization of those functions whose all translates are complete in certain Orlicz space $L^{\\Phi}(\\mathbb{R})$. As a consequence, we identified those discrete sets $\\Lambda \\subseteq \\mathbb{R}$ such that there exists a function in $L^{\\Phi}(\\mathbb{R})$ whose $\\Lambda$-translates are complete. We then prove the completeness of all translates of any simple step function in other Orlicz spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-28T12:44:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E30",
      "42A65",
      "42C30"
    ],
    "keywords": [
      "orlicz space",
      "translates",
      "completeness",
      "simple step function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}