{"paper":{"title":"On the square root of Poisson kernel in $\\delta$-hyperbolic spaces and some aspects of boundary representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Adrien Boyer","submitted_at":"2015-05-04T18:12:59Z","abstract_excerpt":"In this note, we prove a theorem \\`a la Fatou for the square root of Poisson Kernel in the context of quasi-convex cocompact discrete groups of isometries of $\\delta$-hyperbolic spaces. As a corollary we show that some matrix coefficients of boundary representations cannot satisfy \\emph{the weak inequality of Harish-Chandra}. Nevertheless, such matrix coefficients satisfy an inequality which can be viewed as a particular case of the inequality coming from \\emph{property RD} for boundary representations. The inequality established in this paper is based on a uniform bound which appears in the p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00739","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"}