{
  "abstract": "We study the positive Helson form $h_0[a,b]=\\sum_{m,n\\ge1}α(mn)a_n\\overline{b_m}$ on the finitely supported sequences $c_{00}\\subset\\ell^2(\\mathbb{N})$, where $α(n)=\\int_{\\mathbb{R}}n^{-s}dμ(s)<\\infty$ for a finite positive Borel measure $μ$. Under the Carleman condition $\\sum_{k\\ge1}α(4^k)^{-1/(2k)}=\\infty$, closability of $h_0$ is equivalent to $\\sqrt{n}α(n)\\to0$, and hence to $μ((-\\infty,1/2])=0$. For measures concentrated on $(1/2,\\infty)$, we identify the closure of the operator $N_0a=\\sum_{n\\ge1}a_nn^{-s}$, defined on $c_{00}$, with its maximal realization from $\\ell^2(\\mathbb{N})$ to $L^2(μ)$. We further prove that the sequences $a\\in c_{00}$ satisfying $\\sum_{n\\ge1}a_n/\\sqrt{n}=0$ form an operator core for the positive self-adjoint operator associated with the closure of $h_0$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12252",
  "author_total": 3,
  "authors": [
    {
      "name": "Tengfei Ma"
    },
    {
      "name": "Yufeng Lu"
    },
    {
      "name": "Chao Zu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ez183kygfjzdj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12252",
  "fulltext_url": null,
  "id": "ez183kygfjzdj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12252",
  "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": "W7221127292",
  "pdf_url": "https://arxiv.org/pdf/2610.12252",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ez183kygfjzdj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.12252",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12252"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Unbounded Helson Forms with a Moment Representation",
  "title_text": "Unbounded Helson Forms with a Moment Representation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/ez183kygfjzdj",
  "venue": "arXiv",
  "versions": []
}