{
  "abstract": "We introduce and study a pseudo-differential operator $W^α$, defined via the $p$-adic Mellin transformation, acting on real- or complex-valued functions on the multiplicative group of the field of $p$-adic numbers. The operator $W^α$ is maximally dissipative. An estimate of its heat kernel is given.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.23256",
  "author_total": 3,
  "authors": [
    {
      "name": "Alexandra V. Antoniouk"
    },
    {
      "name": "Anatoly N. Kochubei"
    },
    {
      "name": "Mariia V. Serdiuk"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/04s0p2xpsn0d4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.23256",
  "fulltext_url": null,
  "id": "04s0p2xpsn0d4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.23256",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2610|advanced mathematical theories"
    ]
  ],
  "openalex": "W7171571697",
  "pdf_url": "https://arxiv.org/pdf/2607.23256",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/04s0p2xpsn0d4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2607.23256",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.23256"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A Pseudo-Differential Operator of the $p$-Adic Multiplicative Calculus",
  "title_text": "A Pseudo-Differential Operator of the p-Adic Multiplicative Calculus",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/04s0p2xpsn0d4",
  "venue": "arXiv",
  "versions": []
}