{"paper":{"title":"Clifford Coherent State Transforms on Spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jo\\~ao P. Nunes, Jos\\'e Mour\\~ao, Pei Dang, Tao Qian","submitted_at":"2016-12-05T11:50:22Z","abstract_excerpt":"We introduce a one-parameter family of transforms, $U^t_{(m)}$, $t>0$, from the Hilbert space of Clifford algebra valued square integrable functions on the $m$--dimensional sphere, $L^2(S^{m},d\\sigma_{m})\\otimes \\mathbb{C}_{m+1}$, to the Hilbert spaces, ${\\mathcal M}L^2(\\mathbb{R}^{m+1} \\setminus \\{0\\},d\\mu_t)$, of monogenic functions on $\\mathbb{R}^{m+1}\\setminus \\{0\\}$ which are square integrable with respect to appropriate measures, $d\\mu_t$. We prove that these transforms are unitary isomorphisms of the Hilbert spaces and are extensions of the Segal-Bargman coherent state transform, $U_{(1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01319","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"}