{"paper":{"title":"Fourier transform of nonlinear images of self-similar measures: qualitative aspects","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Amlan Banaji, Han Yu","submitted_at":"2026-06-08T17:05:29Z","abstract_excerpt":"The goal of this paper is to establish polynomial Fourier decay for images of self-similar measures $\\mu$ on $\\mathbb{R}^k$ under sufficiently nonlinear real-analytic maps $f \\colon \\mathbb{R}^k \\to \\mathbb{R}^d$. For example, we prove that if $f$ is analytic on $\\mathbb{R}^k$, its graph does not lie in an affine hyperplane in $\\mathbb{R}^{k+d}$, and $\\mu$ is not supported in an affine hyperplane in $\\mathbb{R}^k$, then the image measure has polynomial Fourier decay. Key steps in the proof include establishing a uniform Lojasiewicz-type inequality for self-similar measures, and using the decay"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09743","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/2606.09743/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"}