This book lays the foundations of differential calculus in infinite dimensions and discusses those applications in infinite dimensional differential geometry and global analysis not involving Sobolev completions and fixed point theory. The approach is simple: a mapping is called smooth if it maps smooth curves to smooth curves. Up to Frechet spaces, this notion of smoothness coincides with all known reasonable concepts. In the same spirit, calculus of holomorphic mappings (including Hartogs' theorem and holomorphic uniform boundedness theorems) and calculus of real analytic mappings are developed. Existence of smooth partitions of unity, the foundations of manifold theory in infinite dimensions, the relation between tangent vectors and derivations, and differential forms are discussed thoroughly. Special emphasis is given to the notion of regular infinite dimensional Lie groups.Many applications of this theory are included: manifolds of smooth mappings, groups of diffeomorphisms, geodesics on spaces of Riemannian metrics, direct limit manifolds, perturbation theory of operators, and differentiability questions of infinite dimensional representations.
| ISBN: | 9780821807804 |
| Publication date: | 30th September 1997 |
| Author: | Andreas Kriegl, Peter W Michor |
| Publisher: | American Mathematical Society |
| Format: | Hardback |
| Pagination: | 618 pages |
| Series: | Mathematical Surveys and Monographs |
| Genres: |
Algebraic topology Differential and Riemannian geometry Calculus and mathematical analysis |
This book lays the foundations of differential calculus in infinite dimensions and discusses those applications in infinite dimensional differential geometry and global analysis not involving Sobolev completions and fixed point theory. The approach is simple: a mapping is called smooth if it maps smooth curves to smooth curves. Up to Frechet spaces, this notion of smoothness coincides with all known reasonable concepts. In the same spirit, calculus of holomorphic mappings (including Hartogs' theorem and holomorphic uniform boundedness theorems) and calculus of real analytic mappings are developed. Existence of smooth partitions of unity, the foundations of manifold theory in infinite dimensions, the relation between tangent vectors and derivations, and differential forms are discussed thoroughly. Special emphasis is given to the notion of regular infinite dimensional Lie groups.Many applications of this theory are included: manifolds of smooth mappings, groups of diffeomorphisms, geodesics on spaces of Riemannian metrics, direct limit manifolds, perturbation theory of operators, and differentiability questions of infinite dimensional representations.
The Convenient Setting of Global Analysis features in the following genres: Algebraic topology, Differential and Riemannian geometry, Calculus and mathematical analysis
The Convenient Setting of Global Analysis is available in Hardback, Paperback
The Convenient Setting of Global Analysis was written by Andreas Kriegl, Peter W Michor and published by American Mathematical Society
The Convenient Setting of Global Analysis has 618 pages
Yes it is part of Mathematical Surveys and Monographs series