2020/05/30 by Helge Glöckner, Glockner, Helge · 1 citation
Mathematics · #22E65 #22E67 #46E40 #46M05 #46T05 #46T10 #54C20 (primary) #54D40 #57N20 #57R18 #58B05 #58C25 (secondary) #77R10 #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2006.00254
openalex publication_date 2020/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For suitable finite-dimensional smooth manifolds M (possibly with various kinds of boundary or corners), locally convex topological vector spaces F and non-negative integers k, we construct continuous linear operators Sn from the space of F-valued k times continuously differentiable functions on M to the corresponding space of smooth functions such that Sn(f) converges to f in Ck(M,F) as n tends to infinity, uniformly for f in compact subsets of Ck(M,F). We also study the existence of continuous linear right inverses for restriction maps from Ck(M,F) to Ck(L,F) if L is a closed subset of M, endowed with a Ck-manifold structure turning the inclusion map from L to M into a Ck-map. Moreover, we construct continuous linear right inverses for restriction operators between spaces of sections in vector bundles in many situations, and smooth local right inverses for restriction operators between manifolds of mappings. We also obtain smoothing results for sections in fibre bundles.