{
  "abstract": "We derive a canonical functional model for a pair of isometric operators $(V_1, V_2)$ acting on a Hilbert space $\\mathcal{H}$ that satisfy the automorphic covariance relation $V_1 V_2 = V_2 φ(V_1)$, where $φ$ is an automorphism of the unit disk $\\mathbb{D}$. This extends the classical Bercovici--Douglas--Foias functional model for commuting isometric pairs to a dynamically twisted setting. When both $V_1$ and $V_2$ are pure isometries (shifts), the model simplifies to $(M_z, M_Θ W_φ^*)$ acting on $H^2(\\mathcal{F})$, where $W_φ$ is a unitary weighted composition operator on the Hardy space $H^2$ and $Θ\\in H^\\infty(\\mathbb{D}, \\mathcal{B}(\\mathcal{F}))$ is an operator-valued inner function such that $M_Θ$ is a shift. As an application, we establish a complete unitary classification theorem for automorphically covariant isometric pairs by identifying a complete set of joint unitary invariants. Notably, our results are novel even in the special case of rotation automorphisms ($V_1 V_2 = q V_2 V_1$ with $|q| = 1$).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26773",
  "author_total": 2,
  "authors": [
    {
      "name": "Sourav Ghosh"
    },
    {
      "name": "Haripada Sau"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8a0ry85e2g6p7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26773",
  "fulltext_url": null,
  "id": "8a0ry85e2g6p7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26773",
  "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.CV"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7223042808",
  "pdf_url": "https://arxiv.org/pdf/2610.26773",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8a0ry85e2g6p7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:31:00Z",
      "native_id": "2610.26773",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26773"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Functional Model for Isometric Pairs Satisfying an Automorphic Covariance Relation - I",
  "title_text": "Functional Model for Isometric Pairs Satisfying an Automorphic Covariance Relation - I",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:47Z",
  "url": "https://research.draconitic.com/paper/8a0ry85e2g6p7",
  "venue": "arXiv",
  "versions": []
}