{"paper":{"title":"Dolgopyat's method and the fractal uncertainty principle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DS","math.SP","nlin.CD"],"primary_cat":"math.CA","authors_text":"Long Jin, Semyon Dyatlov","submitted_at":"2017-02-13T03:45:32Z","abstract_excerpt":"We show a fractal uncertainty principle with exponent $1/2-\\delta+\\epsilon$, $\\epsilon>0$, for Ahflors-David regular subsets of $\\mathbb R$ of dimension $\\delta\\in (0,1)$. This improves over the volume bound $1/2-\\delta$, and $\\epsilon$ is estimated explicitly in terms of the regularity constant of the set. The proof uses a version of techniques originating in the works of Dolgopyat, Naud, and Stoyanov on spectral radii of transfer operators. Here the group invariance of the set is replaced by its fractal structure. As an application, we quantify the result of Naud on spectral gaps for convex "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03619","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"}