{
  "abstract": "We study endpoint mapping properties of low-energy wave operators for Schrödinger operators $H=-Δ+V$ on $\\mathbb R^n$, $n\\ge3$. In dimension four, we prove that a zero-energy resonance prevents $L^1$ boundedness, whether or not zero is also an eigenvalue, under $|V(x)|\\lesssim\\langle x\\rangle^{-β}$ with $β>10$. For a zero-energy eigenvalue without a resonance, we obtain a complete low-energy $L^p$ classification in every dimension $n\\ge3$ under $β>n+4$. In particular, $L^\\infty$ boundedness is equivalent to the vanishing of the zeroth, first, and harmonic second moments of $Vψ$ for every zero-energy eigenfunction $ψ$. The proof identifies the finite-rank obstruction and shows that the remaining eigenvalue correction cannot cancel its critical asymptotic profiles. The same conclusions hold for the full wave operators when the corresponding high-energy bounds are available.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00869",
  "author_total": 3,
  "authors": [
    {
      "name": "Han Cheng"
    },
    {
      "name": "Changxing Miao"
    },
    {
      "name": "Xiaohua Yao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f4b7n6p8z13bg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00869",
  "fulltext_url": null,
  "id": "f4b7n6p8z13bg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00869",
  "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-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7215873476",
  "pdf_url": "https://arxiv.org/pdf/2610.00869",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f4b7n6p8z13bg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2610.00869",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00869"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Endpoint Mapping Properties of Wave Operators for Schrödinger Operators in Dimensions $n\\ge3$",
  "title_text": "Endpoint Mapping Properties of Wave Operators for Schrödinger Operators in Dimensions n≥3",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/f4b7n6p8z13bg",
  "venue": "arXiv",
  "versions": []
}