{
  "abstract": "A remarkable theorem of S. Alesker, S. Artstein-Avidan, and V. Milman characterizes the Fourier transform on $\\mathbb{R}^n$ as, in essence, the unique transformation on the space of tempered distributions that exchanges convolution with pointwise multiplication. In this paper, we extend this perspective to the setting of the Heisenberg group $\\He$, focusing on functions taking values in a separable Hilbert space $\\Hi$. We establish a characterization of the group Fourier transform on $\\He$ in terms of convolution. More precisely, we characterize the group Fourier transform on $L^1(\\He,\\Hi)$ and $L^2(\\He,\\Hi)$. In addition, we obtain a similar characterization for the group Fourier transform of $\\Hi$-valued Schwartz class functions on the Heisenberg group.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03267",
  "author_total": 3,
  "authors": [
    {
      "name": "Satyajyoti Achar"
    },
    {
      "name": "Md Hasan Ali Biswas"
    },
    {
      "name": "Ramesh Manna"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2ahq1brrgxxgw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03267",
  "fulltext_url": null,
  "id": "2ahq1brrgxxgw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03267",
  "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.CA"
    ],
    [
      "arxiv",
      "math.FA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03267",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2ahq1brrgxxgw.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03267",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03267"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Characterization of the group Fourier transform of Hilbert space Valued functions",
  "title_text": "Characterization of the group Fourier transform of Hilbert space Valued functions",
  "type": "preprint",
  "updated_at": "2026-11-03T12:21:14Z",
  "url": "https://research.draconitic.com/paper/2ahq1brrgxxgw",
  "venue": "arXiv",
  "versions": []
}