{"paper":{"title":"Duality in Segal-Bargmann Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Todd Kemp, William E. Gryc","submitted_at":"2012-11-26T18:44:09Z","abstract_excerpt":"For $\\alpha>0$, the Bargmann projection $P_\\alpha$ is the orthogonal projection from $L^2(\\gamma_\\alpha)$ onto the holomorphic subspace $L^2_{hol}(\\gamma_\\alpha)$, where $\\gamma_\\alpha$ is the standard Gaussian probability measure on $\\C^n$ with variance $(2\\alpha)^{-n}$. The space $L^2_{hol}(\\gamma_\\alpha)$ is classically known as the Segal-Bargmann space. We show that $P_\\alpha$ extends to a bounded operator on $L^p(\\gamma_{\\alpha p/2})$, and calculate the exact norm of this scaled $L^p$ Bargmann projection. We use this to show that the dual space of the $L^p$-Segal-Bargmann space $L^p_{hol}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6061","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"}