{
  "abstract": "In this work, we study a family of transmutation operators for the Sturm--Liouville operator in impedance form with an integrable potential satisfying a smallness condition. Specifically, we consider transmutations associated with the pair \\[\\textbf{L}_r=\\frac{1}{r^2 (x)}\\frac{d}{dx}r^2 (x)\\frac{d}{dx} \\quad \\text{and} \\quad \\textbf{M}=\\frac{d^2}{dx^2}. \\] We extend existing results by showing that a particular transmutation operator on $W^{3,1} (-a,a)$ can be represented in integral form, where the kernel function satisfies a corresponding Goursat problem. We establish the existence of this kernel using two distinct approaches: the classical method of successive approximations and an application of Picard's theorem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28772",
  "author_total": 2,
  "authors": [
    {
      "name": "Briceyda B. Delgado"
    },
    {
      "name": "F. Ayça Çetinkaya"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8fcq2etakxpy7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28772",
  "fulltext_url": null,
  "id": "8fcq2etakxpy7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28772",
  "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.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7214387087",
  "pdf_url": "https://arxiv.org/pdf/2609.28772",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8fcq2etakxpy7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.28772",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28772"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Transmutation operators for the Sturm--Liouville equation in impedance form with an integrable potential",
  "title_text": "Transmutation operators for the Sturm--Liouville equation in impedance form with an integrable potential",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/8fcq2etakxpy7",
  "venue": "arXiv",
  "versions": []
}