Differentiable mappings between weighted restricted products

2014/09/22 by Boris Walter, Walter, Boris
Mathematics · #26E15 #26E20 (Secondary) #46E10 (Primary) 46T20 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:26E15 #msc:26E20 #msc:46E10 #msc:46T20

paper · pdf · doi:10.48550/arxiv.1409.6195

arxiv created 2016/01/13 · arxiv updated 2016/01/14

Abstract

In this paper, we introduce restricted products for families of locally convex spaces and formulate criteria ensuring that mappings into such products are continuous or smooth. As a special case, can define restricted products of weighted function spaces and obtain results concerning continuity and differentiability properties of natural non-linear mappings between such spaces. These concepts and results are the basis for the study of weighted vector fields on Riemannian manifolds in a subsequent work (see [B. Walter, "Weighted diffeomorphism groups of Riemannian manifolds", arXiv: 1601.02834]), which serve as modelling spaces for suitable infinite-dimensional Lie groups of diffeomorphisms.

Citations

• Weighted diffeomorphism groups of Riemannian manifolds

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• Weighted spaces of vector-valued functions and the ε-product
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• Automatic continuity and weighted composition operators between spaces of vector-valued differentiable functions
• Examples of differentiable mappings into non-locally convex spaces