{"paper":{"title":"Segal-Bargmann transform and Paley-Wiener theorems on Heisenberg motion groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Suparna Sen","submitted_at":"2010-08-16T05:58:16Z","abstract_excerpt":"We study the Segal-Bargmann transform on the Heisenberg motion groups $\\mathbb{H}^n \\ltimes K,$ where $\\mathbb{H}^n$ is the Heisenberg group and $K$ is a compact subgroup of $U(n)$ such that $(K,\\mathbb{H}^n)$ is a Gelfand pair. The Poisson integrals associated to the Laplacian for the Heisenberg motion group are also characterized using Gutzmer's formulae. Explicitly realizing certain unitary irreducible representations of $\\mathbb{H}^n \\ltimes K,$ we prove the Plancherel theorem. A Paley-Wiener type theorem is proved using complexified representations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2577","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"}