{
  "abstract": "This paper provides a complete characterization of the spectrum, point spectrum, continuous spectrum, and residual spectrum of bounded convolution operators acting on the non-separable space $σ_\\infty$, the dual of the Hahn sequence space. Because standard duality and separability-based techniques fail in this setting, a linear functional approach is employed with the fine spectral decomposition of the unilateral shift operator. Furthermore, as a major application of this methodology, we establish a complete description of the fine spectrum for operator polynomials acting on general sequence spaces without requiring separability. This result provides a unified framework that subsumes classical spectral determinations for general banded triangular matrices across various sequence spaces and enables the explicit computation of fine spectrum on non-separable spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02919",
  "author_total": 2,
  "authors": [
    {
      "name": "Sayan Saha"
    },
    {
      "name": "Arnab Patra"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8yh66fzcgjfy7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02919",
  "fulltext_url": null,
  "id": "8yh66fzcgjfy7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02919",
  "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",
      "2613|Approximation Theory and Sequence Spaces"
    ]
  ],
  "openalex": "W7220383555",
  "pdf_url": "https://arxiv.org/pdf/2610.02919",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8yh66fzcgjfy7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.02919",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02919"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Spectral Properties of Convolution Operators on Non-Separable Sequence Spaces",
  "title_text": "Spectral Properties of Convolution Operators on Non-Separable Sequence Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/8yh66fzcgjfy7",
  "venue": "arXiv",
  "versions": []
}