Differentiable mappings between weighted restricted products
Functional Analysis
2016-01-14 v2
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.
Cite
@article{arxiv.1409.6195,
title = {Differentiable mappings between weighted restricted products},
author = {Boris Walter},
journal= {arXiv preprint arXiv:1409.6195},
year = {2016}
}