{
  "id": "1502.05994",
  "version": "v1",
  "published": "2014-12-16T09:46:49.000Z",
  "updated": "2014-12-16T09:46:49.000Z",
  "title": "On the equivalence between the sets of the trigonometric polynomials",
  "authors": [
    "Krystian Kazaniecki",
    "Michał Wojciechowski"
  ],
  "comment": "6 pages",
  "categories": [
    "math.CA",
    "math.FA"
  ],
  "abstract": "In this paper we construct an injection from the linear space of trigonometric polynomials defined on $\\mathbb{T}^d$ with bounded degrees with respect to each variable to a suitable linear subspace $L^1_E\\subset L^1(\\mathbb{T})$. We give such a quantitative condition on $L^1_E$ that this injection is a isomorphism of a Banach spaces equipped with $L^1$ norm and the norm of the isomorphism is independent on the dimension $d$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-16T09:46:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "equivalence",
      "linear space",
      "suitable linear subspace",
      "isomorphism",
      "quantitative condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}