{"paper":{"title":"The Bargmann transform and powers of harmonic oscillator on Gelfand-Shilov subspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Antonio Galbis, Carmen Fernandez, Joachim Toft","submitted_at":"2015-07-17T07:17:28Z","abstract_excerpt":"We consider the counter images $\\maclJ (\\rr d)$ and $\\maclJ _0(\\rr d)$ of entire functions with exponential and almost exponential bounds, respectively, under the Bargmann transform, and we characterize them by estimates of powers of the harmonic oscillator. We also consider the Pilipovi{\\'c} spaces $\\bsycalS _s(\\rr d)$ and $\\bsySig _s(\\rr d)$ when $0<s<1/2$ and deduce their images under the Bargmann transform."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04850","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"}