{
  "abstract": "For a prime number $p > 2$, let $\\bm{0} \\in D \\subset \\mathbb{Z}^n$ be a $p$-element digit set satisfying $ \\mathcal{Z}(\\widehatδ_D) =\\cup_{j=1}^{p-1}(\\frac{j}{p}\\bm{a}+\\mathbb{Z}^{n}) $ for some \\( \\bm{a} \\in \\{ (i_1, \\dots, i_n)^t : i_k \\in [1, p-1] \\cap \\mathbb{Z}, 1\\leq k\\leq n \\} \\), where $\\mathcal{Z}(\\widehatδ_D)$ is the zero set of the Fourier transform of $δ_D$. Let $Q$ be an integer expansive diagonal matrix in $\\mathbb{R}^{n}$, the self-affine measure $μ_{Q,D}$ is defined by \\[ μ_{Q,D}(\\cdot) = \\frac{1}{\\#D} \\sum_{d \\in D} μ_{Q,D}(Q(\\cdot) - d). \\] In this paper, we first provide sufficient condition for a maximal orthogonal family $E_Λ=\\{ e^{-2πi \\langle λ, x \\rangle} : λ\\in Λ\\subset\\mathbb{R}^{n}\\}$ to be an orthogonal basis of $L^2(μ_{Q,D})$ when $Q = p\\operatorname{diag}[q, \\dots, q]$ with $q\\geq 1$. Then we obtain necessary and sufficient conditions for the integer matrix $R$ such that $E_Λ$ and $E_{RΛ}$ are both orthogonal basis of $L^{2}(μ_{Q,D})$. Furthermore, for $Q = p\\operatorname{diag}[l_1, \\dots, l_n]$ with $|l_1 \\dots l_n| > 1$, we give a necessary and sufficient condition under which the real diagonal matrix is the second type spectral eigenmatrices of $μ_{Q,D}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07468",
  "author_total": 2,
  "authors": [
    {
      "name": "Jia-Long Chen"
    },
    {
      "name": "Wen-Hui Ai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/983pt4rsndr6d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07468",
  "fulltext_url": null,
  "id": "983pt4rsndr6d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07468",
  "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": "W7212078602",
  "pdf_url": "https://arxiv.org/pdf/2609.07468",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/983pt4rsndr6d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07468",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07468"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Spectral structure and eigenmatrices of self-affine measures with $p$-digits in $ \\bf{\\mathbb{R}^{n}} $",
  "title_text": "Spectral structure and eigenmatrices of self-affine measures with p-digits in $ \\bf{\\mathbb{R}^{n}} $",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/983pt4rsndr6d",
  "venue": "arXiv",
  "versions": []
}