{
  "id": "1811.09182",
  "version": "v1",
  "published": "2018-11-22T14:12:44.000Z",
  "updated": "2018-11-22T14:12:44.000Z",
  "title": "$\\mathcal{H}_p$-theory of general Dirichlet series",
  "authors": [
    "Andreas Defant",
    "Ingo Schoolmann"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Inspired by results of Bayart on ordinary Dirichlet series $\\sum a_n n^{-s}$, the main purpose of this article is to start an $\\mathcal{H}_p$-theory of general Dirichlet series $\\sum a_n e^{-\\lambda_{n}s}$. Whereas the $\\mathcal{H}_p$-theory of ordinary Dirichlet series, in view of an ingenious identification of Bohr, can be seen as a sub-theory of Fourier analysis on the infinite dimensional torus $\\mathbb{T}^\\infty$, the $\\mathcal{H}_p$-theory of general Dirichlet series is build as a sub-theory of Fourier analysis on certain compact abelian groups, including the Bohr compactification $\\overline{\\mathbb{R}}$ of the reals. Our approach allows to extend various important facts on Hardy spaces of ordinary Dirichlet series to the much wider setting of $\\mathcal{H}_p$-spaces of general Dirichlet series.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-22T14:12:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "general dirichlet series",
      "ordinary dirichlet series",
      "fourier analysis",
      "infinite dimensional torus",
      "compact abelian groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}