{
  "abstract": "This paper presents some results for the slice regular functions and hyperholomorphic functions theories, as consequences of new relationships between the global operator $G$, Fueter operator $\\mathcal D$ and Laplacian operator $Δ_{\\mathbb{R}^{4}}$. Although our results are presented in the quaternionic setting, a fine interpretation in terms of vector calculus of the slice regular function theory yields an interesting relationship between this theory and harmonic analysis. Moreover, we introduce and study a submodule of the hyperholomorphic functions associated to the unit ball $\\mathbb B^4(0,1)$ given in terms of new series expansions of these functions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.19496",
  "author_total": 4,
  "authors": [
    {
      "name": "José Oscar González-Cervantes"
    },
    {
      "name": "Daniel González-Campos"
    },
    {
      "name": "Juan Bory-Reyes"
    },
    {
      "name": "Baruch Schneider"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3x0vvj6a9p899.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.19496",
  "fulltext_url": null,
  "id": "3x0vvj6a9p899",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.19496",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CV"
    ],
    [
      "openalex",
      "2604|Algebraic and Geometric Analysis"
    ]
  ],
  "openalex": "W7170183436",
  "pdf_url": "https://arxiv.org/pdf/2607.19496",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3x0vvj6a9p899.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2607.19496",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.19496"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A connection between quaternionic slice regular and Fueter hyperholormorphic functions",
  "title_text": "A connection between quaternionic slice regular and Fueter hyperholormorphic functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/3x0vvj6a9p899",
  "venue": "arXiv",
  "versions": []
}