{
  "abstract": "In 1998, Jorgensen and Pedersen constructed the first example of a singular continuous spectral measure. Precisely, they proved that the self-similar measure generated by the iterated function system $\\{\\frac{x-1}{4},\\frac{x+1}{4}\\}$ with equal weights, denoted by $μ_{1/4}$, is a spectral measure with a spectrum $Λ_4$, called the canonical spectrum,\\[ Λ_4 := \\set{ \\sum_{j=0}^{m-1}\\varepsilon_j4^j: m\\ge 1,\\ \\varepsilon_j\\in\\{0,1\\} }. \\] For $f\\in L^1(μ_{1/4})$, let $S_n f$ be the $n$-th partial sum of its Mock Fourier series with respect to $Λ_4$. We prove that the associated maximal operator $S^{\\ast}f=\\sup_n|S_n f|$ is of weak type $(1,1)$. Consequently, $S_n f\\to f$ $μ_{1/4}$-almost everywhere on $\\supp(μ_{1/4})$. This solves a long-standing open problem of Strichartz \\cite[p.~341]{Str06}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.27796",
  "author_total": 2,
  "authors": [
    {
      "name": "Min-Wei Tang"
    },
    {
      "name": "Zhi-Yi Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f9nyz8jfc0baz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.27796",
  "fulltext_url": null,
  "id": "f9nyz8jfc0baz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.27796",
  "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",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7171924474",
  "pdf_url": "https://arxiv.org/pdf/2607.27796",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f9nyz8jfc0baz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2607.27796",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.27796"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Almost everywhere convergence of mock Fourier series for the middle-fourth Cantor measure",
  "title_text": "Almost everywhere convergence of mock Fourier series for the middle-fourth Cantor measure",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/f9nyz8jfc0baz",
  "venue": "arXiv",
  "versions": []
}