{"paper":{"title":"The exponential law for spaces of test functions and diffeomorphism groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.DG"],"primary_cat":"math.FA","authors_text":"Andreas Kriegl, Armin Rainer, Peter W. Michor","submitted_at":"2014-11-03T13:42:52Z","abstract_excerpt":"We prove the exponential law $\\mathcal A(E \\times F, G) \\cong \\mathcal A(E,\\mathcal A(F,G))$ (bornological isomorphism) for the following classes $\\mathcal A$ of test functions: $\\mathcal B$ (globally bounded derivatives), $W^{\\infty,p}$ (globally $p$-integrable derivatives), $\\mathcal S$ (Schwartz space), $\\mathcal D$ (compact sport, $\\mathcal B^{[M]}$ (globally Denjoy_Carleman), $W^{[M],p}$ (Sobolev_Denjoy_Carleman), $\\mathcal S_{[L]}^{[M]}$ (Gelfand_Shilov), and $\\mathcal D^{[M]}$. Here $E, F, G$ are convenient vector spaces (finite dimensional in the cases of $W^{\\infty,p}$, $\\mathcal D$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0483","kind":"arxiv","version":3},"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"}