{"paper":{"title":"Polynomial Fourier decay for fractal measures and their pushforwards","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Amlan Banaji, Simon Baker","submitted_at":"2024-01-02T15:18:07Z","abstract_excerpt":"We prove that the pushforwards of a very general class of fractal measures $\\mu$ on $\\mathbb{R}^d$ under a large family of non-linear maps $F \\colon \\mathbb{R}^d \\to \\mathbb{R}$ exhibit polynomial Fourier decay: there exist $C,\\eta>0$ such that $|\\widehat{F\\mu}(\\xi)|\\leq C|\\xi|^{-\\eta}$ for all $\\xi\\neq 0$. Using this, we prove that if $\\Phi = \\{ \\varphi_a \\colon [0,1] \\to [0,1] \\}_{a \\in \\mathcal{A}}$ is an iterated function system consisting of analytic contractions, and there exists $a \\in \\mathcal{A}$ such that $\\varphi_a$ is not an affine map, then every non-atomic self-conformal measure "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.01241","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2401.01241/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"}