{
  "id": "1902.02073",
  "version": "v1",
  "published": "2019-02-06T09:07:20.000Z",
  "updated": "2019-02-06T09:07:20.000Z",
  "title": "Hardy spaces of general Dirichlet series - a survey",
  "authors": [
    "Andreas Defant",
    "Ingo Schoolmann"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "The main purpose of this article is to survey on some key elements of a recent $\\mathcal{H}_p$-theory of general Dirichlet series $\\sum a_n e^{-\\lambda_{n}s}$, which was mainly inspired by the work of Bayart and Helson on ordinary Dirichlet series $\\sum a_n n^{-s}$. In view of an ingenious identification of Bohr, the $\\mathcal{H}_p$-theory of ordinary Dirichlet series can be seen as a sub-theory of Fourier analysis on the infinite dimensional torus $\\mathbb{T}^\\infty$. Extending these ideas, the $\\mathcal{H}_p$-theory of $\\lambda$-Dirichlet series is build as a sub-theory of Fourier analysis on what we call $\\lambda$-Dirichlet groups. A number of problems is added.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-06T09:07:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "general dirichlet series",
      "hardy spaces",
      "ordinary dirichlet series",
      "fourier analysis",
      "infinite dimensional torus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}