{
  "abstract": "We study the linearization, with respect to zeroth-order perturbations, of the local Dirichlet-to-Neumann map of a formally self-adjoint elliptic operator $P=-Δ_g+Q$ on a compact Riemannian manifold $(M,g)$ of dimension $n\\geq 2$ with boundary, where $Q$ is of order at most one. Near a boundary point where the boundary, metric, and $P$ are analytic, we show that the linearized map is a classical analytic pseudodifferential operator of order $-1$ if and only if the zeroth-order perturbation $q$ extends analytically across the boundary. We also prove that local boundary data in an arbitrary open analytic boundary patch determines $q$ locally. In particular, if the measurement set meets every connected component of $M$, the local linearized DN map is injective on $L^\\infty$ perturbations. Finally, we obtain a global completeness result for products of pairs of solutions whose boundary traces are supported in the measurement set. The global recovery proceeds by local steps using Runge approximation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19288",
  "author_total": 3,
  "authors": [
    {
      "name": "Leonard Busch"
    },
    {
      "name": "Tony Liimatainen"
    },
    {
      "name": "Gunther Uhlmann"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cr5j99esd3sjz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19288",
  "fulltext_url": null,
  "id": "cr5j99esd3sjz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19288",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2610|Numerical methods in inverse problems"
    ]
  ],
  "openalex": "W7222186571",
  "pdf_url": "https://arxiv.org/pdf/2610.19288",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cr5j99esd3sjz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19288",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19288"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Density of Products of Solutions and the Linearized Calderón Problem in an Analytic Background",
  "title_text": "Density of Products of Solutions and the Linearized Calderón Problem in an Analytic Background",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/cr5j99esd3sjz",
  "venue": "arXiv",
  "versions": []
}