{
  "abstract": "In this paper, we show that for every p>2, there is an orthonormal basis of spherical harmonics on Sn with n>=2 which achieves the maximal Lp norm growth. More precisely, one basis achieves this growth for all p<=2(n+1)/(n-1), and another for all p>=2(n+1)/(n-1). This extends the results in Han (arXiv:1404.5016) to all dimensions and all p>2, and improves the positive density subsequence there to a whole basis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14023",
  "author_total": 1,
  "authors": [
    {
      "name": "Xiaolong Han"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fn0jg6azgxvza.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14023",
  "fulltext_url": null,
  "id": "fn0jg6azgxvza",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14023",
  "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.CA"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2612|Mathematical Approximation and Integration"
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  ],
  "openalex": "W7213372906",
  "pdf_url": "https://arxiv.org/pdf/2609.14023",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fn0jg6azgxvza.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.14023",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14023"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Spherical harmonics with maximal Lp norm growth",
  "title_text": "Spherical harmonics with maximal Lp norm growth",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/fn0jg6azgxvza",
  "venue": "arXiv",
  "versions": []
}