{
  "abstract": "We prove the logarithmic Weyl law predicted by Connes and Moscovici for large positive eigenvalues of the distinguished self-adjoint extension of the operator $P=-\\partial_x(x^2-1)\\partial_x-4π^2x^2$ on the real line. More precisely, we use the WKB method and show a Bohr-Sommerfeld quantization rule characterizing sufficiently large eigenvalues. A particular difficulty is that the associated $h$-dependent Lagrangian submanifolds are non-compact, which requires a renormalization of the action integral. Furthermore, to deal with the degeneracy of the coefficients at $x =\\pm 1$, we use a quasimode matching argument based on radial estimates and Lagrangian regularity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32639",
  "author_total": 3,
  "authors": [
    {
      "name": "Kouichi Taira"
    },
    {
      "name": "Max Willems"
    },
    {
      "name": "Michał Wrochna"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dgaxnkkzzbg7g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32639",
  "fulltext_url": null,
  "id": "dgaxnkkzzbg7g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32639",
  "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": "W7214808795",
  "pdf_url": "https://arxiv.org/pdf/2609.32639",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dgaxnkkzzbg7g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.32639",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32639"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Large eigenvalues of the Connes-Moscovici operator",
  "title_text": "Large eigenvalues of the Connes-Moscovici operator",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/dgaxnkkzzbg7g",
  "venue": "arXiv",
  "versions": []
}