{
  "abstract": "In the paper, we prove a recursive version of the weighted Sidelnikov-Welch inequality for real and complex unit vectors. Unlike the classical form, which gives a direct lower bound for a fixed even power sum, our inequality relates two consecutive even power sums. Iteration yields the usual weighted Sidelnikov-Welch bound. We apply this estimate to maximal relative projection constants. If $\\mathbb{K}^m$ admits a maximal equiangular tight frame with $M_{\\mathbb K}$ vectors, then for every integer $k\\geq1$, $$ λ_{\\mathbb K}(kM_{\\mathbb K}-m,kM_{\\mathbb K}) = λ_{\\mathbb K}(m)-\\frac{2m}{kM_{\\mathbb K}}+1. $$ Moreover, the maximal value is realized by an equiangular tight frame when $k=1$ and by a biangular tight frame when $k\\geq2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29422",
  "author_total": 2,
  "authors": [
    {
      "name": "Beata Deregowska"
    },
    {
      "name": "Barbara Lewandowska"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6x910v88dxsgz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29422",
  "fulltext_url": null,
  "id": "6x910v88dxsgz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29422",
  "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.FA"
    ],
    [
      "openalex",
      "2604|Mathematical Analysis and Transform Methods"
    ]
  ],
  "openalex": "W7214345996",
  "pdf_url": "https://arxiv.org/pdf/2609.29422",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6x910v88dxsgz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.29422",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29422"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "From Sidelnikov-Welch bounds to projection constants",
  "title_text": "From Sidelnikov-Welch bounds to projection constants",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/6x910v88dxsgz",
  "venue": "arXiv",
  "versions": []
}