{"paper":{"title":"On the characterization of Gelfand-Shilov-Roumieu spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mihai Pascu","submitted_at":"2013-06-04T14:14:45Z","abstract_excerpt":"Generalized $\\mathbf{m}$-Gelfand-Shilov-Roumieu vector spaces $\\mathcal{S}_{\\mathbf{m}}(\\mathbf{X})$ are introduced. Here $\\mathbf{m} = (m^{(1)},...,m^{(n)})$, $\\mathbf{X}=(X_{1},...,X_{n})$ and $m^{(1)},...,m^{(n)}$ are sequences of positive real numbers and $X_{1},...,X_{n}$ are operators in a Hilbert space. Conditions are given on the sequences $m^{(1)},...,m^{(n)}$ and on the operators $X_{1},...,X_{n}$ so that the equality $S_{\\mathbf{m}}(\\mathbf{X}) = S_{m^{(1)}}(X_{1})\\cap ... \\cap{S}_{m^{(n)}}(X_{n})$ is valid. As a corollary we obtain a new proof of a characterization theorem for clas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0800","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"}