Walter, Boris: Weighted diffeomorphism groups of Banach spaces and non-compact manifolds and weighted mapping groups. 2014
Inhalt
- Introduction
- Preliminaries and notation
- Weighted function spaces
- Definition and examples
- Topological and uniform structure
- Composition on weighted functions and superposition operators
- Composition with a multilinear map
- Composition of weighted functions with bounded functions
- Composition of weighted functions with an analytic map
- Superposition with functions defined on a product
- Weighted maps into locally convex spaces
- Lie groups of weighted diffeomorphisms on Banach spaces
- Weighted diffeomorphisms and endomorphisms
- Lie group structures on weighted diffeomorphisms
- The Lie group structure of DiffW
- On decreasing weighted diffeomorphisms and dense subgroups
- On diffeomorphisms that are weighted endomorphisms
- Regularity
- Lie groups of weighted diffeomorphisms on Riemannian manifolds
- Weighted restricted products
- Restricted products for locally convex spaces with uniformly parameterized seminorms
- Restricted products of weighted functions
- Simultaneous superposition and multiplication
- Simultaneous composition and inversion
- Spaces of weighted vector fields on manifolds
- Definition and properties
- Simultaneous composition, inversion and superposition with Riemannian exponential map and logarithm
- Construction of weights on manifolds
- Diffeomorphisms on Riemannian manifolds
- Integration of certain Lie algebras of vector fields
- Lie group structures on weighted mapping groups
- Differential calculus
- Differential calculus of maps between locally convex spaces
- Fréchet differentiability
- Relation between the differential calculi
- Some facts concerning ordinary differential equations
- Locally convex Lie groups and manifolds
- Quasi-inversion in algebras
- Notation
- Index