{"paper":{"title":"On a distinctive property of Fourier bases associated with $N$- Bernoulli Convolutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Xing-Gang He, Zhi-Yi Wu, Zi-Chao Chi","submitted_at":"2025-05-31T03:07:44Z","abstract_excerpt":"A distinctive problem of harmonic analysis on $\\R$ with respect to a Borel probability measure $\\mu$ is identifying all $t\\in\\R$ such that both \\[\\left\\{e^{-2\\pi i\\lambda x}: \\lambda\\in\\Lambda\\right\\}\\quad\\text{and}\\quad \\left\\{e^{-2\\pi i\\lambda x}: \\lambda\\in t\\Lambda\\right\\}\\] form orthonormal bases of the space $L^2(\\mu)$. Currently, this phenomenon has been observed only in certain singular measures. It is deeply connected to the convergence of Mock Fourier series with respect to the aforementioned bases. In this paper, we apply classical number theory to solve the general conjecture and b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.00364","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/2506.00364/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"}