{
  "abstract": "We introduce a new class of commutative associative algebras whose structural constants are linear operators acting in a linear topological space. An analogue of the theory of monogenic functions is developed for such algebras. It is shown that the components of monogenic functions satisfy second-order operator-differential equations. This approach provides a constructive method for obtaining solutions of various partial differential and integro-differential equations. Several illustrative examples are presented.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12478",
  "author_total": 1,
  "authors": [
    {
      "name": "Vitalii Shpakivskyi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1afy4t3yerjsv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12478",
  "fulltext_url": null,
  "id": "1afy4t3yerjsv",
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  "landing_url": "https://arxiv.org/abs/2610.12478",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
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      "arxiv",
      "math-ph"
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  "pdf_url": "https://arxiv.org/pdf/2610.12478",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1afy4t3yerjsv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:36Z",
      "native_id": "2610.12478",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12478"
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  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Operator Algebras and Their Applications",
  "title_text": "Operator Algebras and Their Applications",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/1afy4t3yerjsv",
  "venue": "arXiv",
  "versions": []
}