{
  "abstract": "We prove that every infinite compact abelian group $G$ admits a countably infinite proper set $E\\subset\\widehat G$ that is strongly small-2 but not Riesz. More precisely, $|α|*|β|$ is absolutely continuous for all $α,β\\in M_E(G)$, whereas $M_E(G)$ contains a singular complex measure of total mass one with exact Fourier support $E$ whose convolution square belongs to $L^2(G)$. When the image of the doubling map on $\\widehat G$ is infinite, $E$ may moreover be chosen so that $\\#(E\\cap(γ-E))<\\infty$ for every $γ$ and $E\\cap(-E)=\\{0\\}$. When that image is finite, we reduce the problem to a nonrectangular construction on the Walsh group, for which $E\\cap(E+γ)$ is finite at every nonzero shift.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12628",
  "author_total": 1,
  "authors": [
    {
      "name": "Przemysław Ohrysko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0mjrpeagm0caz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12628",
  "fulltext_url": null,
  "id": "0mjrpeagm0caz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12628",
  "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.FA"
    ],
    [
      "openalex",
      "2604|Mathematical Analysis and Transform Methods"
    ]
  ],
  "openalex": "W7212869342",
  "pdf_url": "https://arxiv.org/pdf/2609.12628",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0mjrpeagm0caz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2609.12628",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12628"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Strongly small-2 sets that are not Riesz sets on compact abelian groups",
  "title_text": "Strongly small-2 sets that are not Riesz sets on compact abelian groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/0mjrpeagm0caz",
  "venue": "arXiv",
  "versions": []
}