Weighted diffeomorphism groups of Banach spaces and weighted mapping groups
Functional Analysis
2014-09-23 v3
Abstract
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 weighted diffeomorphisms on a Banach space. Further, we also construct certain types of weighted mapping groups. Both the weighted diffeomorphism groups and the weighted mapping groups are shown to be regular Lie groups in Milnor's sense. We also discuss semidirect products of the former groups. Moreover, we study the integrability of Lie algebras of certain vector fields.
Keywords
Cite
@article{arxiv.1006.5580,
title = {Weighted diffeomorphism groups of Banach spaces and weighted mapping groups},
author = {Boris Walter},
journal= {arXiv preprint arXiv:1006.5580},
year = {2014}
}
Comments
In the proof of Lemma 3.3.13, a claim was made that needed a rigorous proof. Fitted that in as Lemma 3.3.13, the old Lemma 3.3.13 became 3.3.14