The Convenient Setting of Global Analysis: 53.S - Brossura

Kriegl, Andreas; Michor, Peter W.

Brossura

ISBN 10: 1470478935 ISBN 13: 9781470478933

Casa editrice: Amer Mathematical Society, 1997

Riassunto

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.

Dettagli dell'edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 1997
• Lingua: Inglese
• ISBN 10: 1470478935
• ISBN 13: 9781470478933
• Rilegatura: Copertina flessibile
• Numero di pagine: 618
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile