{
  "abstract": "We prove a variant of the $L^2$ Fourier restriction inequality for non-degenerate curves in the setting of orthonormal systems. To achieve this, we develop a Hilbert space approach to studying the $L^2$ theory for Fourier restriction for curves. Our arguments also rely on novel $L^p$-improving bounds for associated convolution operators, which take averages over neighbourhoods of cones generated by the curve. The $L^p$-improving bound are established using a variant of the high-low method, in particular using induction-on-scale.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02596",
  "author_total": 3,
  "authors": [
    {
      "name": "Jean-Claude Cuenin"
    },
    {
      "name": "Jacob Denson"
    },
    {
      "name": "Jonathan Hickman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8w1y04m2s6nnf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02596",
  "fulltext_url": null,
  "id": "8w1y04m2s6nnf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02596",
  "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",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7220384395",
  "pdf_url": "https://arxiv.org/pdf/2610.02596",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8w1y04m2s6nnf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.02596",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02596"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Space curve Fourier restriction for orthonormal functions",
  "title_text": "Space curve Fourier restriction for orthonormal functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/8w1y04m2s6nnf",
  "venue": "arXiv",
  "versions": []
}