{
  "abstract": "We first revisit the Nevanlinna condition for representing measures of Herglotz-Nevanlinna functions in two variables and give a general operator-theoretic criterion for extremality. We then derive an explicit formula for the representing measure of a real rational Herglotz-Nevanlinna function in two variables, and combine it with the extremality criterion to obtain a family of extreme elements in the full cone of Nevanlinna measures. The family includes examples with reducible denominators, and these yield counterexamples to the irreducibility assertion in a conjecture of Knese. We then characterize reducibility within this family both algebraically and geometrically.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02476",
  "author_total": 2,
  "authors": [
    {
      "name": "Ludvig Fagrell"
    },
    {
      "name": "Annemarie Luger"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1t0ddsgw6tjnv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02476",
  "fulltext_url": null,
  "id": "1t0ddsgw6tjnv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02476",
  "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|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7220457072",
  "pdf_url": "https://arxiv.org/pdf/2610.02476",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1t0ddsgw6tjnv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.02476",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02476"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Real rational Herglotz-Nevanlinna functions in two variables and a class of extremals",
  "title_text": "Real rational Herglotz-Nevanlinna functions in two variables and a class of extremals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/1t0ddsgw6tjnv",
  "venue": "arXiv",
  "versions": []
}