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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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2401.01241","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-01-02T15:18:07Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"25a40246dff8298e19c0f43da4a87fd52a44cc9920516ea96c10436c0850f669","abstract_canon_sha256":"fa557ef0e954c4ae808941cb2c1b203c3260537ee58349a69a3379d50f3040d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:58:58.840576Z","signature_b64":"6urHV6QzOad/jpwwQsJIHszMH7bYRHqQP1avjR5Qng4o9wVpqWQEXSCCU1m97EAoU0YWJ12JysBmSsI5TFKcBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f683c141d4091357218c4fb42bda556fdc4461d3a4cd35fda9eab4f453ac6c21","last_reissued_at":"2026-07-05T10:58:58.840067Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:58:58.840067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\xi\\neq 0$. 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