Approximation of Continuously Differentiable Functions

Description

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. 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