Weighted diffeomorphism groups of Banach spaces and weighted mapping groups
In this work, we construct and study certain classes of infinite-dimensional Lie groups that are modelled on weighted function spaces. In particular, we construct a Lie group of diffeomorphisms, for each Banach space X and each set of weights on X containing the constant weights. We also construct certain types of “weighted mapping groups”. These are Lie groups modelled on weighted function spaces of the form , where G is a given (finite- or infinite-dimensional) Lie group. Both the weighted...