{"paper":{"title":"On the dimension of orthogonal projections of self-similar measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Amir Algom, Pablo Shmerkin","submitted_at":"2024-07-23T08:09:35Z","abstract_excerpt":"Let $\\nu$ be a self similar measure on $\\mathbb{R}^d$, $d\\geq 2$, and let $\\pi$ be an orthogonal projection onto a $k$-dimensional subspace. We formulate a criterion on the action of the group generated by the orthogonal parts of the IFS on $\\pi$, and show that it ensures the dimension of $\\pi \\nu$ is preserved; this significantly refines previous results by Hochman-Shmerkin (2012) and Falconer-Jin (2014), and is sharp for projections to lines and hyperplanes. A key ingredient in the proof is an application of a restricted projection theorem of Gan-Guo-Wang (2024)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.16262","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/2407.16262/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"}