Differentiable mappings between weighted restricted products

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.