{
  "abstract": "Given $A,B\\in B\\left(H\\right)_{+}$, we consider the existence and uniqueness of a positive operator $C\\in B\\left(H\\right)_{+}$ such that \\[ \\left(I+mA+nB+mnC\\right)^{-1}=\\int_{\\left[0,1\\right]^{2}}s^{m}t^{n}dE\\left(s,t\\right),\\quad m,n\\geq0, \\] for a positive operator-valued measure $E$. This is a joint Hausdorff moment problem. Without $C$, it holds if and only if $AB=BA$. In dimension two we give a complete criterion for noncommuting pairs. In higher finite dimensions, nonexistence is generic. Under certain spectral and cyclicity assumptions, we obtain a necessary and sufficient condition on arbitrary Hilbert spaces. The completion is unique in this case. We also classify these pairs up to unitary equivalence. The class includes irreducible infinite-dimensional examples, even with continuous spectrum.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03081",
  "author_total": 1,
  "authors": [
    {
      "name": "James Tian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0egqc5j4w16cj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03081",
  "fulltext_url": null,
  "id": "0egqc5j4w16cj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03081",
  "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"
    ],
    [
      "arxiv",
      "math.SP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03081",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0egqc5j4w16cj.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03081",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03081"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Joint Moments of Bilinear Resolvents",
  "title_text": "Joint Moments of Bilinear Resolvents",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/0egqc5j4w16cj",
  "venue": "arXiv",
  "versions": []
}