{"paper":{"title":"On composition of Segal-Bargmann transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Abdelhadi Benahmadi, Allal Ghanmi, Kamal Diki","submitted_at":"2016-11-04T11:43:36Z","abstract_excerpt":"We introduce and discuss some basic properties of some integral transforms in the framework of specific functional Hilbert spaces, the holomorphic Bargmann-Fock spaces on $\\mathbb{C}$ and $\\mathbb{C}^2$ and the slice hyperholomorphic Bargmann-Fock space on $\\mathbb{H}$. The first one is a natural integral transform mapping isometrically the standard Hilbert space on the real line into the two-dimensional Bargmann-Fock space. It is obtained as composition of the one and two dimensional Segal-Bargmann transforms and reduces further to an extremely integral operator that looks like a composition "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01338","kind":"arxiv","version":2},"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"}