{
  "abstract": "We characterize diagonal profiles admitting universal real trigonometric Fourier series with factors in $\\mathcal E_s=\\bigcap_{p>s}\\ell^p$ and $\\ell^{s,q}$, $2\\le s<\\infty$, $1\\le q\\le\\infty$. For nonincreasing profiles we obtain exact dyadic criteria and logarithmic endpoints. For independently regular odd/even sine/cosine branches we characterize simultaneous subseries, sign, and rearrangement universality for finite almost-everywhere targets. One function in every $L^p$, $1\\le p<2$, supplies the coefficients. A separation example admits this realization although every compatible nonincreasing majorant with bounded relative cost belongs to $\\ell^1$. Residue-class decompositions extend the criterion; a weakest-model condition permits extended-real rearrangement targets. A Walsh--Paley counterpart yields the same diagonal multiplier thresholds for ternary $\\{0,\\pm1\\}$-universality, together with a Fourier--Walsh realization. Trigonometric realization uses Pogosyan's majorant theorem; the multiplier, factorization, projection-transfer, separation, and Walsh Fourier-origin arguments are proved here.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27348",
  "author_total": 1,
  "authors": [
    {
      "name": "Sergo A. Episkoposian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dj3hxx2jyxs9e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27348",
  "fulltext_url": null,
  "id": "dj3hxx2jyxs9e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27348",
  "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.CA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.27348",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dj3hxx2jyxs9e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.27348",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27348"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Diagonal and branchwise criteria for universal Fourier series",
  "title_text": "Diagonal and branchwise criteria for universal Fourier series",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/dj3hxx2jyxs9e",
  "venue": "arXiv",
  "versions": []
}