{"paper":{"title":"Cesaro convergence of spherical averages for measure-preserving actions of Markov semigroups and groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.OA"],"primary_cat":"math.DS","authors_text":"Alexander Bufetov, Alexey Klimenko, Mikhail Khristoforov","submitted_at":"2011-01-28T05:57:33Z","abstract_excerpt":"Cesaro convergence of spherical averages is proven for measure-preserving actions of Markov semigroups and groups. Convergence in the mean is established for functions in $L^p$, $1\\le p<\\infty$, and pointwise convergence for functions in $L^\\infty$. In particular, for measure-preserving actions of word hyperbolic groups (in the sense of Gromov) we obtain Cesaro convergence of spherical averages with respect to any symmetric set of generators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.5459","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":""},"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"}