{"paper":{"title":"Invariant measures on homogeneous spaces, with applications to function spaces and lattice counting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Bernhard Kr\\\"otz, Eitan Sayag, Henrik Schlichtkrull","submitted_at":"2010-04-12T12:53:28Z","abstract_excerpt":"Let G be a real reductive group and G/H a unimodular homogeneous G space with\na closed connected subgroup H. We establish estimates for the invariant measure\non G/H. Using these, we prove that all smooth vectors in the Banach\nrepresentation L^p(G/H) of G are functions that vanish at infinity if and only\nif G/H is of reductive type. An application to lattice counting on G/H is\npresented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.1942","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"}