{
  "id": "2411.15379",
  "version": "v2",
  "published": "2024-11-22T23:44:35.000Z",
  "updated": "2024-12-25T18:49:40.000Z",
  "title": "Mixed-Fourier-norm spaces and holomorphic functions",
  "authors": [
    "Zhirayr Avetisyan",
    "Alexey Karapetyants"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We describe a general framework of functional and Fourier analysis on domains with a free action of an Abelian Lie group $G$. Namely, on a domain of the form $G\\times Y$ we introduce the appropriate spaces of distributions and measurable functions, establishing their most basic properties. Then we consider the half-Fourier transform $f(x,y)\\mapsto\\hat f(\\xi,y)$ in the first variable, and discuss the behaviour of function spaces on $G\\times Y$ and $\\hat G\\times Y$ under this transform. We introduce general mixed-Fourier-norm spaces on $G\\times Y$, and the subspaces of holomorphic functions among them, and give an explicit descriptions of the Fourier images of these spaces.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-12-25T18:49:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30H20",
      "46E30",
      "46E15"
    ],
    "keywords": [
      "holomorphic functions",
      "abelian lie group",
      "general mixed-fourier-norm spaces",
      "free action",
      "fourier images"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}