{
  "abstract": "Noninjective multiplication symbols allow commuting operators to mix function values along their fibers, while Hölder regularity constrains this mixing at branch points. We study these operators on the Banach algebra $A_β$, $0<β<1$, defined by a restricted interval-variation condition. For $u(t)=t(1-t)$, we determine the full commutant $\\{M_u\\}'=\\mathscr C_β$, including operators whose reflection coefficients need not belong to $A_β$. Separately, we characterize the operator-norm closure $J_β$ of the regular multiplication--reflection subalgebra of $\\mathscr C_β$, obtain two-sided norm-distance estimates, and find a complemented copy of $\\ell^\\infty/c_0$ in the Banach-space quotient $\\mathscr C_β/J_β$. Every $T\\in\\mathscr C_β$ satisfies $σ(T)=σ_{\\mathrm{ap}}(T)=σ_{\\mathrm{usf}}(T)=σ_{\\mathrm{ess}}(T)$, and Fredholmness is equivalent to invertibility. For multipliers with finitely many full bi-Lipschitz branches, we also characterize their full commutants and establish the same spectral equalities for every commuting operator. For the regular finite-branch algebra, we establish an exact norm-closure criterion using weighted local Hölder defects and separate row-difference conditions, even when several folds share a level.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36217",
  "author_total": 3,
  "authors": [
    {
      "name": "Hülya Duru"
    },
    {
      "name": "Serkan İlter"
    },
    {
      "name": "Arkady Kitover"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e8hwsvwbxwewd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36217",
  "fulltext_url": null,
  "id": "e8hwsvwbxwewd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36217",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7224107323",
  "pdf_url": "https://arxiv.org/pdf/2610.36217",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e8hwsvwbxwewd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.36217",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36217"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Finite-Branch Multipliers on a Hölder Algebra: Commutants, Norm Closures, and Essential Spectra",
  "title_text": "Finite-Branch Multipliers on a Hölder Algebra: Commutants, Norm Closures, and Essential Spectra",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/e8hwsvwbxwewd",
  "venue": "arXiv",
  "versions": []
}