Approximation of Continuously Differentiable Functions

José G. Llavona (Eds.)9780444701282, 0444701281, 9780080872414

This self-contained book brings together the important results of a rapidly growing area. As a starting point it presents the classic results of the theory. The book covers such results as: the extension of Wells’ theorem and Aron’s theorem for the fine topology of order m; extension of Bernstein’s and Weierstrass’ theorems for infinite dimensional Banach spaces; extension of Nachbin’s and Whitney’s theorem for infinite dimensional Banach spaces; automatic continuity of homomorphisms in algebras of continuously differentiable functions, etc.

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Table of contents :
Content:
Editor
Page ii

Edited by
Page iii

Copyright page
Page iv

Dedication
Page v

foreword
Pages vii-x
José G. Llavona

Chapter 0 Preliminary Results
Pages 1-22

Chapter 1 Approximation of Smooth Functions on Manifolds
Pages 23-51

Chapter 2 Simultaneous Approximation of Smooth Functions
Pages 53-63

Chapter 3 Polynomial Approximation of Differentiable Functions
Pages 65-77

Chapter 4 Weakly Continuous Functions on Banach Spaces
Pages 79-113

Chapter 5 Approximation of Weakly Uniformly Differentiable Functions
Pages 115-125

Chapter 6 Approximation for the Compact-Open Topology
Pages 127-132

Chapter 7 Approximation of Weakly Differentiable Functions
Pages 133-149

Chapter 8 Spaces of Differentiable Functions and the Approximation Property
Pages 151-159

Chapter 9 Polynomial Algebras of Continuously Differentiable Functions
Pages 161-167

Chapter 10 On the Closure of Modules of Continuously Differentiable Functions
Pages 169-176

Chapter 11 Homomorphisms Between Algebras of Uniformly Weakly Differentiable Functions
Pages 177-194

Chapter 12 The Paley-Wiener-Schwartz Theorem in Infinite Dimension
Pages 195-207

Appendix I Whitney’s Spectral Theorem
Pages 209-219

References
Pages 221-233

Index
Pages 235-238

Index of Symbols
Pages 239-241