{"paper":{"title":"Regularity properties of free multiplicative convolution on the positive line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hong Chang Ji","submitted_at":"2019-03-06T11:32:44Z","abstract_excerpt":"Given two nondegenerate Borel probability measures $\\mu$ and $\\nu$ on $\\mathbb{R}_{+}=[0,\\infty)$, we prove that their free multiplicative convolution $\\mu\\boxtimes\\nu$ has zero singular continuous part and its absolutely continuous part has a density bounded by $x^{-1}$. When $\\mu$ and $\\nu$ are compactly supported Jacobi measures on $(0,\\infty)$ having power law behavior with exponents in $(-1,1)$, we prove that $\\mu\\boxtimes\\nu$ is another Jacobi measure whose density has square root decay at the edges of its support."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.02326","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/1903.02326/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"}