{"paper":{"title":"Boundedness and compactness of composition operators on Segal-Bargmann spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Trieu Le","submitted_at":"2011-11-30T20:05:04Z","abstract_excerpt":"For $E$ a Hilbert space, let $\\mathcal{H}(E)$ denote the Segal-Bargmann space (also known as the Fock space) over $E$, which is a reproducing kernel Hilbert space with kernel $K(x,y)=\\exp(< x,y>)$ for $x,y$ in $E$. If $\\phi$ is a mapping on $E$, the composition operator $C_{\\phi}$ is defined by $C_{\\phi}h = h\\circ\\phi$ for $h\\in \\mathcal{H}(E)$ for which $h\\circ\\phi$ also belongs to $\\mathcal{H}(E)$. We determine necessary and sufficient conditions for the boundedness and compactness of $C_{\\phi}$. Our results generalize results obtained earlier by Carswell, MacCluer and Schuster for finite di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.7294","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"}