Approximation of Vector Valued Functions
Elsevier (Publisher)
Published on 10. October 2011
218 pages
978-0-08-087136-3 (ISBN)
Description
This work deals with the many variations of the Stoneileierstrass Theorem for vector-valued functions and some of its applications. The book is largely self-contained. The amount of Functional Analysis required is minimal, except for Chapter 8. The book can be used by graduate students who have taken the usual first-year real and complex analysis courses.
More details
Other editions
Additional editions
Joao B. Prolla
Approximation of Vector Valued Functions
Book
08/1977
Elsevier
€16.09
Article exhausted; check different version
Persons
Content
- Front Cover
- Approximation of Vector Valued Functions
- Copyright Page
- CONTENTS
- PREFACE
- INTRODUCTION
- CHAPTER 1. THE COMPACT-OPEN TOPOLOGY
- § 1. Basic definitions
- § 2. Localizability
- § 3. Preliminary lemmas
- § 4. Stone-Weierstrass Theorem for modules
- § 5. The complex self -adjoint case
- § 6. Submodules of C (X
- E)
- § 7. An example: a theorem of Rudin
- § 8. Bishop's Theorem
- § 9. Vector fibrations
- § 10. Extreme functionals
- § 11. Representation of vector fibrations
- § 12. The approximation property
- Appendix. Non-locally convex spaces
- CHAPTER 2. THE THEOREM OF DIEUDONNE
- CHAPTER 3. EXTENSION THEOREMS
- CHAPTER 4. POLYNOMIAL ALGEBRAS
- § 1. Basic definitions and lemmas
- § 2. Stone-Weierstrass subspaces
- § 3. C(x)-modules
- § 4. Approximation of compact operators
- CHAPTER 5. WEIGHTED APPROXIMATION
- § 1. Definition of Nachbin spaces
- § 2. The Bernstein-Nachbin approximation problem
- § 3. Sufficient conditions for sharp localizability
- § 4. Completeness o f Nachbin spaces
- § 5. Dual spaces of Nachbin spaces
- Appendix. Fundamental weights
- CHAPTER 6. THE SPACE Co (X
- E) with the uniform topology
- CHAPTER 7. THE SPACE Cb ( X
- E) with the strict topology
- CHAPTER 8. THE e-PRODUCT OF L. SCHWARTZ
- § 1. General definitions
- § 2. Spaces of continuous functions
- § 3. The approximation property
- § 4. Mergelyan's Theorem
- § 5. Localiz ation of the approximation property
- CHAPTER 9. NONARCHIMEDEAN APPROXIMATION THEORY
- § 1. Valued fields
- § 2. Kaplansky's Theorem
- § 3. Normed spaces
- § 4. Vector-valued functions
- § 5. Vector fibrations
- § 6. Some applications
- § 7. Bishop's Theorem
- § 8. Tietze Extension Theorem
- § 9. The compact-open topology
- § 10. The nonarchimedean strict topology
- BIBLIOGRAPHY
- SYMBOL INDEX
- INDEX
