Weighted diffeomorphism groups of Banach spaces and weighted mapping groups

Details Weighted diffeomorphism groups of Banach spaces and weighted mapping groups Weighted diffeomorphism groups of Banach spaces and weighted mapping groups

2010-06-29

arxiv.org/abs/1006.5580v1

Mathematics

Functional Analysis

Scientific paper

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.

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