The Convenient Setting of Global Analysis (Mathematical Surveys & Monographs) - Hardcover

Andreas Kriegl

Hardcover

ISBN 10: 0821807803 ISBN 13: 9780821807804

Publisher: American Mathematical Society, 1997

Synopsis

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.

Edition details

• Publisher: American Mathematical Society
• Publication date: 1997
• ISBN 10: 0821807803
• ISBN 13: 9780821807804
• Binding: Hardcover
• Language: English
• Number of pages: 618