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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1206.5045","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-06-22T03:08:08Z","cross_cats_sorted":[],"title_canon_sha256":"0e1aa38808a795f99365a2f936ab5b8b0b4e3b86aa422245911b750fbf53b15d","abstract_canon_sha256":"8834ac79a1962cbeb853643500fe14abab7a2e3f3ea7e89332aa31ad3d5d3204"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:52:52.543799Z","signature_b64":"4u2/YVhvJw4ghJrnFIGMW1HEY2R1GY8AoM4MyUk2z+jBHZH95FojJs/prexWD+nrSZmJ5YW1TjA4eIFrjwzZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8448e0f0b2e099b94e755e20cc403ac20a1a8686ff6d217d46d80e717acb0b0c","last_reissued_at":"2026-05-18T03:52:52.543137Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:52:52.543137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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