{
  "abstract": "We construct a perfect set of uniqueness on the circle carrying a continuous probability measure which annihilates every $H^{(d)}$-set, simultaneously for all finite dimensions d. This gives a strict inclusion between the polar of the compact sets of uniqueness and the polar of the union of the classes $H^{(d)}$, answering a question raised in earlier work on these polars. The construction uses random binary increments of size comparable to the reciprocal of a product of square roots. A Gaussian sampling estimate gives a uniform Fourier-tail bound for all pseudomeasures supported by the resulting set, and also bounded atomic approximation and spectral synthesis. A separate energy estimate, stable under deletion of a small number of increments, yields full support for every limiting quasi-independent image of every positive measure absolutely continuous with respect to the constructed measure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02241",
  "author_total": 1,
  "authors": [
    {
      "name": "Václav Vlasák"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bwra68avvgark.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02241",
  "fulltext_url": null,
  "id": "bwra68avvgark",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02241",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02241",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bwra68avvgark.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02241",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02241"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Separating the Polar of Sets of Uniqueness from the Polars of All $H^{(d)}$-Sets",
  "title_text": "Separating the Polar of Sets of Uniqueness from the Polars of All H^(d)-Sets",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:05Z",
  "url": "https://research.draconitic.com/paper/bwra68avvgark",
  "venue": "arXiv",
  "versions": []
}