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.
Author(s): José G. Llavona (Eds.)
Series: North-Holland Mathematics Studies 130
Publisher: Elsevier Science Ltd
Year: 1986
Language: English
Pages: ii-x, 1-241
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
