{"paper":{"title":"On almost everywhere divergence of Bochner-Riesz means on compact Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Dashan Fan, Xianghong Chen","submitted_at":"2016-01-23T17:23:17Z","abstract_excerpt":"Let $G$ be a connected, simply connected, compact semisimple Lie group of dimension $n$. It has been shown by Clerc \\cite{Clerc1974} that, for any $f\\in L^1(G)$, the Bochner-Riesz mean $S_R^\\delta(f)$ converges almost everywhere to $f$, provided $\\delta>(n-1)/2$. In this paper, we show that, at the critical index $\\delta=(n-1)/2$, there exists an $f\\in L^1(G)$ such that $$\\limsup_{R\\rightarrow\\infty} \\big|S_{R}^{(n-1)/2}(f)(x)\\big|=\\infty, \\ \\text{a.e.}\\ x\\in G.$$ This is an analogue of a well-known result of Kolmogorov \\cite{Kolmogoroff1923} for Fourier series on the circle, and a result of S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06295","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":""},"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"}