{"paper":{"title":"Analytic factorization of Lie group representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Bernhard Kr\\\"otz, Christoph Lienau, Heiko Gimperlein","submitted_at":"2009-10-01T13:59:07Z","abstract_excerpt":"For every moderate growth representation of a real Lie group G on a Frechet space E, we prove a factorization theorem of Dixmier--Malliavin type for the space of analytic vectors E^{\\omega}. There exists a natural algebra of superexponentially decreasing analytic functions A(G), such that E^{\\omega} = A(G) * E^{\\omega}. As a corollary we obtain that E^\\omega coincides with the space of analytic vectors for the Laplace--Beltrami operator on G."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.0177","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"}