The convenient setting of global analysis / Andreas Kriegl, Peter W. Michor.

Format:

Book

Author/Creator:

Kriegl, Andreas, author.

Michor, Peter W., 1949- author.

Series:

Mathematical surveys and monographs ; no. 53.

Mathematical surveys and monographs, 0076-5376 ; volume 53

Language:

English

Subjects (All):

Global analysis (Mathematics).

Physical Description:

1 online resource (631 p.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [1997]

Language Note:

English

Summary:

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.

Contents:

""11. The Real Analytic Exponential Law""""Historical Remarks on Holomorphic and Real Analytic Calculus""; ""Chapter III: Partitions of Unity""; ""12. Differentiability of Finite Order""; ""13. Differentiability of Seminorms""; ""14. Smooth Bump Functions""; ""15. Functions with Globally Bounded Derivatives""; ""16. Smooth Partitions of Unity and Smooth Normality""; ""Chapter IV: Smoothly Realcompact Spaces""; ""17. Basic Concepts and Topological Realcompactness""; ""18. Evaluation Properties of Homomorphisms""; ""19. Stability of Smoothly Realcompact Spaces""

""53. Appendix: Projective Resolutions of Identity on Banach spaces""

Notes:

Description based upon print version of record.

Includes bibliographical references (pages 597-610) and index.

Description based on print version record.

ISBN:

9781470478933

1470478935