{
  "abstract": "In this paper, we obtain a complete classification of Toeplitz + Hankel operators on the vector-valued Hardy space $H^2_{\\mathcal{E}}(\\mathbb{D}^n)$ over the polydisc $\\mathbb{D}^n$ in $\\mathbb{C}^n$ for $n\\geq 1$. We also characterize the paired operators on $L^2(\\mathbb{T}^n)$. Furthermore, we give a complete characterization for the class of essentially Toeplitz + essentially Hankel operators on the vector-valued Hardy space $H^2_{\\mathcal{E}}(\\mathbb{D})$ for finite-dimensional Hilbert space $\\mathcal{E}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.23747",
  "author_total": 3,
  "authors": [
    {
      "name": "Kritika Babbar"
    },
    {
      "name": "Mo Javed"
    },
    {
      "name": "Amit Maji"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dns9p89jpm483.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.23747",
  "fulltext_url": null,
  "id": "dns9p89jpm483",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.23747",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7165773335",
  "pdf_url": "https://arxiv.org/pdf/2606.23747",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dns9p89jpm483.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2606.23747",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.23747"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Generalization of Toeplitz + Hankel operators in the polydisc",
  "title_text": "Generalization of Toeplitz + Hankel operators in the polydisc",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/dns9p89jpm483",
  "venue": "arXiv",
  "versions": []
}