{
  "abstract": "We extend the theory of indefinite Hardy spaces on finite bordered Riemann surfaces to the setting of ramified analytic coverings. Given a finite $n$-sheeted ramified covering $F\\colon S_1\\to S_2$ of finite bordered Riemann surfaces satisfying a spin-compatibility hypothesis, we construct (i) the direct image of a unitary flat vector bundle $\\VxX{1}\\otimes \\Del{1}$ on the double $X_1$ under $F$, taking full account of the ramification divisor $R_F$ and establishing the extension across the branch locus via a local analysis; (ii) a canonical matrix function $G_2$ encoding the parahermitian structure on $X_2$, together with the induced representation $χ_2$ of $\\piX{X_2}{p_0}$; (iii) an explicit isometric isomorphism $ϕ_F\\colon H^{2,J_1(p)}(S_1,\\VxS{1}\\otimes\\Del{1}) \\xrightarrow{\\;\\sim\\;} H^{2,J_2(p)}(S_2,\\VxS{2}\\otimes\\Del{2})$ between the associated Hardy-Kre\\uın spaces, provided that $h^0(X_1,\\VxX{1}\\otimes\\Del{1})=0$ and that the branch locus is disjoint from $\\partial S_2$. We then develop the resulting operator theory in terms of vessels and Bezoutian operators. To each object in the category $\\mathcal{RH}$ of finite bordered surfaces with unitary flat bundles we attach a triangular vessel whose input and output spaces are the Hardy-Kre\\uın spaces on the two surfaces. The Bezoutian of the vessel is expressed as a finite-rank operator on $\\mathcal{H}_2$ whose kernel is built from bounded holomorphic point-evaluation functionals in $\\mathcal{H}_2$ evaluated at the interior ramification images $F(r_ν)\\in S_2$, consistently with the boundary-transversality hypothesis $\\partial S_2\\cap B_F=\\left\\{\\varnothing\\right\\}$. We prove that the assignment $(S,\\Vx{},J)\\mapsto H^{2,J(p)}(S,\\Vx{}\\otimesΔ)$ extends to a covariant functor from $\\mathcal{RH}$ (with ramified morphisms) to the category of Kre\\uın spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.22453",
  "author_total": 1,
  "authors": [
    {
      "name": "A. Zuevsky"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6n1q37bkejry3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.22453",
  "fulltext_url": null,
  "id": "6n1q37bkejry3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.22453",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7165662599",
  "pdf_url": "https://arxiv.org/pdf/2606.22453",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6n1q37bkejry3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2606.22453",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.22453"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Hardy spaces on Riemann surfaces under ramified coverings",
  "title_text": "Hardy spaces on Riemann surfaces under ramified coverings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/6n1q37bkejry3",
  "venue": "arXiv",
  "versions": []
}