{"paper":{"title":"On the Fourier transforms of self-similar measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Masato Tsujii","submitted_at":"2012-12-07T08:14:09Z","abstract_excerpt":"For the Fourier transform $\\mathcal{F}\\mu$ of a general (non-trivial) self-similar measure $\\mu$ on the real line $\\mathbb{R}$, we prove a large deviation estimate \\[ \\lim_{c\\to +0} \\varlimsup_{t\\to \\infty}\\frac{1}{t}\\log (\\mathrm{Leb}\\{x\\in [-e^t, e^t]\\mid |\\mathcal{F}\\mu(\\xi)| \\ge e^{-ct} \\})=0. \\]"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1553","kind":"arxiv","version":2},"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"}