{
  "annotation_id": "2ebf246f-aa31-49c5-b073-8827a54fb3f1",
  "date_created": "2026-02-17T05:53:08.444000Z",
  "date_modified": "2026-02-17T05:53:08.444000Z",
  "file_hash": "8be5da9c7a05cd6e8aab69f340f2f07da79e185e3e37dec8128f59259d59142f",
  "private": false,
  "record": {
    "abstract": "This paper is devoted to the investigation of multidimensional analogues of refined Bohr-type inequalities for bounded holomorphic mappings on the unit polydisc $\\mathbb{D}^n$. We establish a sharp extension of the classical Bohr inequality, proving that the Bohr radius remains $R_n = 1/(3n)$ for the family of holomorphic functions bounded by unity in the multivariate setting. Further, we provide a definitive resolution to the Bohr-Rogosinski phenomenon in several complex variables by determining sharp radii for functional power series involving the class of Schwarz functions $\\omega_{n,m}\\in\\mathcal{B}_{n,m}$ and the local modulus $|f(z)|$. By employing the radial (Euler) derivative operator $Df(z) = \\sum_{k=1}^{n} z_k \\frac{\\partial f(z)}{\\partial z_k}$, we obtain refined growth estimates for derivatives that generalize well-known univariate results to $\\mathbb{C}^n$. Finally, a multidimensional version of the area-based Bohr inequality is established. The optimality of the obtained constants is rigorously verified, demonstrating that all established radii are sharp.",
    "arxiv_id": "2601.06630",
    "authors": [
      "Molla Basir Ahamed",
      "Sujoy Majumder",
      "Nabadwip Sarkar"
    ],
    "categories": [
      "math.CV"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Sharp Bohr-Rogosinski radii for Schwarz functions and Euler operators in C^n",
    "url": "https://arxiv.org/abs/2601.06630",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c93f578c-dc2f-4c47-829b-eca2dea226db",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}