{
  "abstract": "For $P=X_1^2+\\cdots + X_n^2$, let $T_t^Pf(x)$ denote the solution to the linear Schrödinger equation at time $t$. In 1980, Carleson asked for the minimal regularity of an initial data function $f\\in H^s(\\mathbb{R}^n)$ that guarantees pointwise convergence of $T_t^Pf(x)$ to $f(x)$ as $t\\rightarrow 0$. This was resolved by Bourgain, who constructed counterexamples for the Schrödinger maximal operator to show that $s\\geq n/(2(n+1))$ is necessary, and Du and Zhang, who proved that $s> n/(2(n+1))$ is sufficient. Rogers, Vargas, and Vega studied the analogous question for the non-elliptic Schrödinger maximal operator, where $P = X_1^2-X_2^2 \\pm X_3^2\\pm \\cdots \\pm X_n^2$, and proved that, for all $n\\geq 2$, $s\\geq 1/2$ is necessary and $s>1/2$ is sufficient. In this paper, we construct counterexamples for generalizations of the non-elliptic case and prove a necessary condition of $s\\geq 1/2$ for an infinite class of polynomial symbols $P$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30048",
  "author_total": 1,
  "authors": [
    {
      "name": "Rena Chu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bj3d6p077nraa.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30048",
  "fulltext_url": null,
  "id": "bj3d6p077nraa",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30048",
  "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.CA"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7204912699",
  "pdf_url": "https://arxiv.org/pdf/2608.30048",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bj3d6p077nraa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30048",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30048"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Counterexamples for generalizations of the non-elliptic Schrödinger maximal operator",
  "title_text": "Counterexamples for generalizations of the non-elliptic Schrödinger maximal operator",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/bj3d6p077nraa",
  "venue": "arXiv",
  "versions": []
}