{
  "abstract": "We consider composition operators in $L^2(μ)$, where $μ$ is a discrete measure. Our main result shows that, for every integer $p\\ge2$, there exists a non-hyponormal composition operator that generates Stieltjes moment sequences and whose symbol induces a directed graph consisting of a circuit of length $p$ and one infinite branch. In contrast, if the symbol induces a directed graph consisting of one loop and one infinite branch, then the generation of Stieltjes moment sequences does imply subnormality. These two results completely solve the ``moment property implies subnormality'' problem left open in [Adv. Math. 310 (2017), 484-556] for the entire family of one-branch directed graphs with a circuit of arbitrary length. Combining them with the examples in that paper shows that, for directed graphs consisting of one loop and a finite number of infinite branches, $2$ is the smallest number of branches for which the moment property does not imply subnormality. Finally, we construct a noninjective composition operator that generates Stieltjes moment sequences and whose symbol induces a directed graph consisting of one loop, one infinite branch, and one leaf. This operator gives a negative answer to the injectivity problem posed in the aforementioned paper. Both constructions use the Krein and Friedrichs measures of an arbitrary normalized S-indeterminate Stieltjes moment sequence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31173",
  "author_total": 4,
  "authors": [
    {
      "name": "Piotr Budzyński"
    },
    {
      "name": "Zenon Jan Jabłoński"
    },
    {
      "name": "Il Bong Jung"
    },
    {
      "name": "Jan Stochel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8mf00ejmm6ep6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31173",
  "fulltext_url": null,
  "id": "8mf00ejmm6ep6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31173",
  "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.FA"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7214620828",
  "pdf_url": "https://arxiv.org/pdf/2609.31173",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8mf00ejmm6ep6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.31173",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31173"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Solutions to the 'moment property implies subnormality' and injectivity problems for composition operators on one-circuit graphs",
  "title_text": "Solutions to the 'moment property implies subnormality' and injectivity problems for composition operators on one-circuit graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/8mf00ejmm6ep6",
  "venue": "arXiv",
  "versions": []
}