{"paper":{"title":"The space $\\dot{\\mathcal{B}}'$ of distributions vanishing at infinity - duals of tensor products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Eduard A. Nigsch, Norbert Ortner","submitted_at":"2016-04-11T09:05:53Z","abstract_excerpt":"Analogous to L.~Schwartz' study of the space $\\mathcal{D}'(\\mathcal{E})$ of semi-regular distributions we investigate the topological properties of the space $\\mathcal{D}'(\\dot{\\mathcal{B}})$ of semi-regular vanishing distributions and give representations of its dual and of the scalar product with this dual. In order to determine the dual of the space of semi-regular vanishing distributions we generalize and modify a result of A. Grothendieck on the duals of $E \\hat\\otimes F$ if $E$ and $F$ are quasi-complete and $F$ is not necessarily semi-reflexive."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02846","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"}