{
  "abstract": "The Askey-Wilson function $ϕ(x, γ)$ is a meromorphic continuation of the Askey-Wilson polynomials in their spectral variable off the lattice $γ= \\tilde{a} q^m, m \\in \\mathbb{Z}_+$. We show that the analytic part of the Askey-Wilson function $ϕ^{an}(x, \\tilde{a} q^γ)$ is the Laplace transform of a positive measure of total measure $ϕ^{an}(x, s_0) < \\infty$, under certain conditions on the parameters governing the function. We deduce log-convexity of this function, as well as positive-definiteness and an integral formula for a certain intertwining operator associated with the Askey-Wilson operator $L$. This offers a $q$-analogue of several results, in the trigonometric limit due to Sahi-McSwiggen, and in the rational (i.e. Dunkl) limit due to Rösler.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03907",
  "author_total": 1,
  "authors": [
    {
      "name": "Aaron Agulnick"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/94xgqpr7s2erb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03907",
  "fulltext_url": null,
  "id": "94xgqpr7s2erb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03907",
  "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.QA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03907",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/94xgqpr7s2erb.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.03907",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03907"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The Askey-Wilson Function is the Laplace Transform of a Positive Measure",
  "title_text": "The Askey-Wilson Function is the Laplace Transform of a Positive Measure",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/94xgqpr7s2erb",
  "venue": "arXiv",
  "versions": []
}