{
  "abstract": "We study the inverse resonance problem for the one-dimensional Schrödinger operator on the half-line with a compactly supported complex-valued potential and a complex Robin boundary condition \\[ u'(0)-a u(0)=0,\\qquad a\\in\\mathbb C. \\] The proof follows the transformation-operator, entire-function, and Fourier analytic strategy developed by Marletta, Shterenberg and Weikard for the Dirichlet problem \\cite{MSW}. The Dirichlet Jost function $ψ(z,0)$ is replaced by the Robin characteristic function \\[ F_a(z;q)=ψ_x(z,0;q)-aψ(z,0;q). \\] We establish the corresponding large-energy estimates, Hadamard factorization, finite-data stability, and uniqueness results. The principal new feature is that $F_a(z;q)=iz-a+O(1)$ rather than $1+O(z^{-1})$. In the transformation-operator argument the relevant boundary quantity is $B_x(0,t)-aB(0,t)$, together with the scalar term $B(0,0)$. For fixed $a\\in\\mathbb C$, and uniformly for $a$ in bounded subsets of $\\mathbb C$, the resulting inverse resonance estimates have the same qualitative form as those proved in \\cite{MSW} for the Dirichlet problem. In particular, for a fixed Robin parameter $a$, the complete set of Robin eigenvalues and resonances, counted with multiplicity, determines the potential uniquely. The text is produced with the help of AI ChatGPT for Academy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14323",
  "author_total": 1,
  "authors": [
    {
      "name": "Roman Shterenberg"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/drwwfnnfvk95q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14323",
  "fulltext_url": null,
  "id": "drwwfnnfvk95q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14323",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7221818786",
  "pdf_url": "https://arxiv.org/pdf/2610.14323",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/drwwfnnfvk95q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2610.14323",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14323"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Inverse Resonance Problem for the Half-Line Schrödinger Operator with a Complex Robin Boundary Condition",
  "title_text": "Inverse Resonance Problem for the Half-Line Schrödinger Operator with a Complex Robin Boundary Condition",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/drwwfnnfvk95q",
  "venue": "arXiv",
  "versions": []
}