{
  "abstract": "Baxter's classical theorem for orthogonal polynomials on the unit circle establishes that the linear Fourier coefficients of a measure are in $\\ell^1$ if and only if the nonlinear coefficients, i.e., the so-called Verblunsky coefficients, are in $\\ell^1$. However, this equivalence is purely qualitative. We explore possible formulations of such quantitative theorems with norm and Lipschitz estimates for the $SU(2)$-valued nonlinear Fourier transform, for which the analog of Baxter's theorem has been recently obtained. In particular, the highlight of this paper is a number-theoretic construction for the NLFT which proves some negative results in this direction. We also prove a positive result and discuss the limitations of Baxter's method.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01711",
  "author_total": 3,
  "authors": [
    {
      "name": "Michel Alexis"
    },
    {
      "name": "Gevorg Mnatsakanyan"
    },
    {
      "name": "Kristina Oganesyan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9b2sdhbxht11y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01711",
  "fulltext_url": null,
  "id": "9b2sdhbxht11y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01711",
  "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",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7216376403",
  "pdf_url": "https://arxiv.org/pdf/2610.01711",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9b2sdhbxht11y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01711",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01711"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Quantitative possibilities for Baxter's theorem in nonlinear Fourier analysis",
  "title_text": "Quantitative possibilities for Baxter's theorem in nonlinear Fourier analysis",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/9b2sdhbxht11y",
  "venue": "arXiv",
  "versions": []
}