{"paper":{"title":"On the Spectral Properties of a Class of Planar Sierpinski Self-Affine Measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jia-Long Chen, Wen-Hui Ai","submitted_at":"2025-08-28T14:10:46Z","abstract_excerpt":"We investigate the spectral properties of a class of Sierpinski-type self-affine measures defined by\n  \\[\n  \\mu_{M,D}(\\cdot) = p^{-1} \\sum_{d \\in D} \\mu_{M,D}(M(\\cdot) - d),\n  \\]\n  where \\( p \\) is a prime number, \\( M = \\begin{bmatrix}\n  \\rho_1^{-1} & c\n  0 & \\rho_2^{-1}\n  \\end{bmatrix} \\) is a real upper triangular expanding matrix, and \\( D = \\{d_0, d_1, \\cdots, d_{p-1}\\} \\subset \\mathbb{Z}^2 \\) satisfying \\( \\mathcal{Z}(\\widehat{\\delta}_{D}) = \\cup_{j=1}^{p-1} \\left( \\frac{j \\bm{a}}{p} + \\mathbb{Z}^2 \\right) \\) for some \\( \\bm{a} \\in \\mathcal{E}_{p}= \\{ (i_1, i_2)^* : i_1, i_2 \\in [1, p-1]"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.20809","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}