{
  "id": "1807.09734",
  "version": "v1",
  "published": "2018-07-25T17:28:07.000Z",
  "updated": "2018-07-25T17:28:07.000Z",
  "title": "Algebraic structure of continuous, unbounded and integrable functions",
  "authors": [
    "M. Carmen Calderón-Moreno",
    "Pablo J. Gerlach-Mena",
    "José A. Prado-Bassas"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper we state the large linear and algebraic size of the family of unbounded continuous and integrable functions in $[0,+\\infty)$ and of the family of sequences of these functions converging to zero uniformly on compacta and in $L^1$-norm. In addition, we put our attention on how fast can these functions grow, how smooth can they be and how strong can the convergence to zero be.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-25T17:28:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A03",
      "26A15",
      "46E30"
    ],
    "keywords": [
      "integrable functions",
      "algebraic structure",
      "continuous",
      "large linear",
      "functions grow"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}