{
  "abstract": "A gas giant Riemannian metric $g$ on a compact $n$-dimensional manifold-with-boundary $M$ blows up at the boundary $\\partial M$ at the rate $1/x^α$, for $α\\in (0,2)$, where $x \\in C^\\infty(M)$ is a boundary-defining function. Such metrics arise in the modeling of acoustic waves in gaseous planets. De Hoop-Ilmavirta-Kykkänen-Mazzeo [arXiv:2403.05475] showed that, if $α> 2/n$, the Laplace-Beltrami operator $Δ_g$ is essentially self-adjoint and has discrete spectrum. Moreover, its spectrum is stable under truncations of $M$. The proof leverages the 0-calculus of Mazzeo-Melrose. We extend this theory by introducing a 0-transition calculus for studying families of 0-operators. We demonstrate a parametrix construction for $Δ_g$ that is stable under truncations. Using this, we study the behavior of the resolvent of $Δ_g$ under truncation and extend the characterization of the spectrum obtained by de Hoop-Ilmavirta-Kykkänen-Mazzeo. In particular, we prove that (on appropriate functional-analytic domains) simple eigenvalues admit asymptotic expansions in the truncation parameter $ε$ and that the corresponding eigenfunctions admit joint asymptotic expansions in $(ε, x)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04191",
  "author_total": 1,
  "authors": [
    {
      "name": "Andy Yin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/drgqz6eb29z5e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04191",
  "fulltext_url": null,
  "id": "drgqz6eb29z5e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04191",
  "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.AP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04191",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/drgqz6eb29z5e.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04191",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04191"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A transition calculus for 0-pseudodifferential operators with applications to gas giant geometry",
  "title_text": "A transition calculus for 0-pseudodifferential operators with applications to gas giant geometry",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/drgqz6eb29z5e",
  "venue": "arXiv",
  "versions": []
}