2015/12/22 by Natalie Nikitin, Nikitin, Natalie
Mathematics · #22E65 (Primary) 26E20 #46E25 #46E40 #46F05 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:22E65 #msc:26E20 #msc:46E25 #msc:46E40 #msc:46F05
paper · pdf · doi:10.48550/arxiv.1512.07211
53 pages. This article is based on the author's master's thesis "Exponential laws for weighted function spaces and regularity of weighted mapping Groups" advised by Helge Glöckner, University of Paderborn, 2015
arxiv created 2015/12/22 · arxiv updated 2015/12/23
Let E be a locally convex space, U⊆ℝn as well as V⊆ℝm be open and k,l∈ℕ0∪\∞\. Locally convex spaces Ck,l(U× 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 Ck,l(U× V,E)≅ Ck(U,Cl(V,E)). We establish an analogous exponential law Ck,lW1\otimesW2(U× V,E)≅ CkW1(U,ClW2(V,E)) for suitable spaces of weighted Ck,l-maps, as well as an analogue for spaces of weighted continuous functions on locally compact spaces. The results entail that certain Lie groups ClW(U,H) of weighted mappings introduced by B.Walter are Ck-regular, for each Ck-regular Lie group H modeled on a locally convex space and a suitable set of weights W.