{"paper":{"title":"Exponential laws for weighted function spaces and regularity of weighted mapping groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Natalie Nikitin","submitted_at":"2015-12-22T19:36:21Z","abstract_excerpt":"Let $E$ be a locally convex space, $U\\subseteq\\mathbb{R}^n$ as well as $V\\subseteq\\mathbb{R}^m$ be open and $k,l\\in\\mathbb{N}_0\\cup\\left\\{\\infty\\right\\}$. Locally convex spaces $C^{k,l}(U\\times V,E)$ of functions with different degrees of differentiability in the $U$- and $V$-variable were recently studied by H.Alzaareer, who established an exponential law of the form $C^{k,l}(U\\times V,E)\\cong C^k(U,C^l(V,E))$. We establish an analogous exponential law $C^{k,l}_{\\mathcal{W}_1\\otimes\\mathcal{W}_2}(U\\times V,E)\\cong C^k_{\\mathcal{W}_1}(U,C^l_{\\mathcal{W}_2}(V,E))$ for suitable spaces of weighte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07211","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"}