{"paper":{"title":"Fourier decay and absolute continuity for typical homogeneous self-similar measures in ${\\mathbb R}^d$ for $d\\ge 3$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Boris Solomyak","submitted_at":"2025-08-20T13:23:13Z","abstract_excerpt":"We consider iterated function systems (IFS) in ${\\mathbb R}^d$ for $d\\ge 3$ of the form $\\{f_j(x) = \\lambda {\\mathcal O} x + a_j\\}_{j=0}^m$, with $a_0=0$ and $m\\ge 1$. Here $\\lambda\\in (0,1)$ is the contraction ratio and ${\\mathcal O}$ is an orthogonal matrix. Given a positive probability vector $p$, there is a unique invariant (stationary) measure for the IFS, called (in this case) a homogeneous self-similar measure, which we denote $\\mu(\\lambda {\\mathcal O}, {\\mathcal D}, p)$, where ${\\mathcal D} = \\{a_0,\\ldots,a_m\\}$ is the set of ``vector digits''. We obtain two results on Fourier decay fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.14698","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/2508.14698/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"}