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The Convenient Setting of Global Analysis

By Kriegl, Andreas

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Book Id: WPLBN0000696826
Format Type: PDF eBook
File Size: 4.02 MB
Reproduction Date: 2005
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Title: The Convenient Setting of Global Analysis  
Author: Kriegl, Andreas
Volume:
Language: English
Subject: Science., Mathematics, Logic
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Kriegl, A. (n.d.). The Convenient Setting of Global Analysis. Retrieved from http://hawaiilibrary.net/


Description
Mathematics document containing theorems and formulas.

Excerpt
Excerpt: At the very conception of the notion of manifolds, in the Habilitationsschrift [Riemann, 1854], infinite dimensional manifolds were mentioned explicitly: Es giebt indess auch Mannigfaltigkeiten, in welchen die Ortsbestimmung nicht eine endliche Zahl, sondern entweder eine unendliche Reihe oder eine stetige Mannigfaltigkeit von Grossenbestimmungen erfordert. Solche Mannigfaltigkeiten bilden z.B. die moglichen Bestimmungen einer Function fur ein gegebenes Gebiet, die moglichen Gestalten einer raumlichen Figur u.s.w. The purpose of this book is to lay the foundations of infinite dimensional differential geometry. The book [Palais, 1968] and review article [Eells, 1966] have similar titles and treat global analysis mainly on manifolds modeled on Banach...

Table of Contents
Table of Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Chapter I Calculus of Smooth Mappings . . . . . . . . . . . . . . . . . . . . . 7 1. Smooth Curves . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2. Completeness . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3. Smooth Mappings and the Exponential Law . . . . . . . . . . . . . 22 4. The c1-Topology . . . . . . . . . . . . . . . . . . . . . . . . 34 5. Uniform Boundedness Principles and Multilinearity . . . . . . . . . 52 6. Some Spaces of Smooth Functions . . . . . . . . . . . . . . . . . 66 Historical Remarks on Smooth Calculus . . . . . . . . . . . . . . . . 73 Chapter II Calculus of Holomorphic and Real Analytic Mappings . . . . . . . . . 79 7. Calculus of Holomorphic Mappings . . . . . . . . . . . . . . . . . 80 8. Spaces of Holomorphic Mappings and Germs . . . . . . . . . . . . 91 9. Real Analytic Curves . . . . . . . . . . . . . . . . . . . . . . . 97 10. Real Analytic Mappings . . . . . . . . . . . . . . . . . . . . . 101 11. The Real Analytic Exponential Law . . . . . . . . . . . . . . . . 105 Historical Remarks on Holomorphic and Real Analytic Calculus . . . . . 116 Chapter III Partitions of Unity . . . . . . . . . . . . . . . . . . . . . . . . . 117 12. Di erentiability of Finite Order . . . . . . . . . . . . . . . . . . 118 13. Di erentiability of Seminorms . . . . . . . . . . . . . . . . . . 127 14. Smooth Bump Functions . . . . . . . . . . . . . . . . . . . . . 152 15. Functions with Globally Bounded Derivatives . . . . . . . . . . . 159 16. Smooth Partitions of Unity and Smooth Normality . . . . . . . . . 165 Chapter IV Smoothly Realcompact Spaces . . . . . . . . . . . . . . . . . . . . 183 17. Basic Concepts and Topological Realcompactness . . . . . . . . . . 184 18. Evaluation Properties of Homomorphisms . . . . . . . . . . . . . 188 19. Stability of Smoothly Realcompact Spaces . . . . . . . . . . . . . 203 20. Sets on which all Functions are Bounded . . . . . . . . . . . . . . 217 Chapter V Extensions and Liftings of Mappings . . . . . . . . . . . . . . . . . 219 21. Extension and Lifting Properties . . . . . . . . . . . . . . . . . 220 22. Whitney's Extension Theorem Revisited . . . . . . . . . . . . . . 226 23. Frolicher Spaces and Free Convenient Vector Spaces . . . . . . . . . 238 24. Smooth Mappings on Non-Open Domains . . . . . . . . . . . . . 247 25. Real Analytic Mappings on Non-Open Domains . . . . . . . . . . 254 26. Holomorphic Mappings on Non-Open Domains . . . . . . . . . . . 261

 

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