{"paper":{"title":"A Walsh-Quotient Obstruction for Fourier Frames on Odd Reciprocal-Power Bernoulli Convolutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Wei-Jie Wang, Xiao-Ye Fu, Zi-Jian Song","submitted_at":"2026-07-12T03:21:20Z","abstract_excerpt":"We introduce a Walsh-quotient obstruction to study Fourier-frame existence for symmetric two-branch Bernoulli convolutions. Suppose that 0 < rho < 1/2 and rho^{-m} = B for some integer m >= 1 and odd integer B >= 3. We prove that L^2(mu_{rho,d}) admits no Fourier frame. For m = 1, our argument independently proves the non-frame theorem for odd-integer-base Cantor measures and hence resolves Strichartz's long-standing open problem for the middle-third Cantor measure. A contemporaneous independent proof of the case m = 1 was obtained by Pont, Liehr and Taylor. For m > 1, our theorem treats the n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.10547","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.10547/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}