{
  "abstract": "A 2009 preprint [1] proposed transferring a cardinal B-spline factor between the members of a biorthogonal scaling pair. The inverse box convolution is unbounded on L 2 and requires an input condition. For compactly supported data, we prove equivalent Fourier, Sobolev, and local-moment tests for its L 2 existence and a finite inverse formula. For a certified biorthogonal seed, we derive translate Riesz bounds. We then give an explicit rational order-four spline seed with a 19-position dual filter. An exact Bernstein certificate proves the dual scaling function belongs to H 1 ; a finite correlation rank witness establishes functional biorthogonality, and rational Gram bounds yield the transferred pair's squared-norm translate constants 1/48 and 48. A strict Fourier-decay bound and the Cohen-Daubechies-Feauveau cross-scale criterion prove dual Riesz wavelet bases of L 2 (R). This coefficient choice repairs a failure of the degree-minimal symmetric complement: we prove its unique algebraic mask has no compactly supported L 2 dual for every spline order m ≥ 4. The order-four filters alone therefore give a counterexample to inferring functions from perfect reconstruction. Daubechies D8 and D24 seeds give further certified transfers, including full-scale wavelet bases. The spline transfer, Bézout construction, and general cross-scale criterion have precedents in He and Cohen-Daubechies-Feauveau; our claims concern the stated inverse-domain characterization, explicit rational design and certificates, and uniform obstruction within the specified minimal class.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Mehmet Ersoy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3ahg6y8f8h4p4.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "3ahg6y8f8h4p4",
  "issns": [],
  "landing_url": "https://hal.science/hal-05803266v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05803266/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3ahg6y8f8h4p4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:58Z",
      "native_id": "hal-05803266",
      "source": "hal",
      "url": "https://hal.science/hal-05803266v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.math",
      "subfield": "general"
    }
  ],
  "title": "Biorthogonal Spline-Wavelet Transfers: An L 2 Criterion, a Rational Construction, and a Minimal-Mask Obstruction",
  "title_text": "Biorthogonal Spline-Wavelet Transfers: An L 2 Criterion, a Rational Construction, and a Minimal-Mask Obstruction",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:58Z",
  "url": "https://research.draconitic.com/paper/3ahg6y8f8h4p4",
  "venue": "HAL",
  "versions": []
}