{"paper":{"title":"Uniform pointwise bounds for Matrix coefficients of unitary representations on semidirect products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Zhenqi Jenny Wang","submitted_at":"2012-06-22T03:08:08Z","abstract_excerpt":"Let $k$ be a local field of characteristic 0, and let $G$ be a connected semisimple almost $k$-algebraic group. Suppose rank$_kG\\geq 1$ and $\\rho$ is an excellent representation of $G$ on a finite dimensional $k$-vector space $V$. We construct uniform pointwise bounds for the $K$-finite matrix coefficients restricted on $G$ of all unitary representations of the semi-direct product $G\\ltimes_\\rho V$ without non-trivial $V$-fixed vectors. These bounds turn out to be sharper than the bounds obtained from $G$ itself for some cases. As an application, we discuss a simple method of calculating Kazhd"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5045","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"}