{"paper":{"title":"Fourier transform of nonlinear images of self-similar measures: quantitative 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":"2025-03-10T16:29:39Z","abstract_excerpt":"This paper relates to the Fourier decay properties of images of self-similar measures $\\mu$ on $\\mathbb{R}^k$ under nonlinear smooth maps $f \\colon \\mathbb{R}^k \\to \\mathbb{R}$. For example, we prove that if the linear parts of the similarities defining $\\mu$ commute and the graph of $f$ has nonvanishing Gaussian curvature, then the Fourier dimension of the image measure is at least $\\max\\left\\{ \\frac{2(2\\kappa_2 - k)}{4 + 2\\kappa_* - k} , 0 \\right\\}$, where $\\kappa_2$ is the lower correlation dimension of $\\mu$ and $\\kappa_*$ is the Assouad dimension of the support of $\\mu$. Under some additi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.07508","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/2503.07508/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"}