Approximation of Continuously Differentiable Functions ( Volume 130 )

Publication series ：Volume 130

Author： Llavona   J. G.  

Publisher： Elsevier Science‎

Publication year： 1986

E-ISBN: 9780080872414

P-ISBN(Paperback): 9780444701282

P-ISBN(Hardback):  9780444701282

Subject： O174.1 Real, real function

Language： ENG

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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.

Chapter

Front Cover

pp.：  1 – 4

Approximation of Continuously Differentiable Functions

pp.：  4 – 5

Copyright Page

pp.：  5 – 12

Foreword

pp.：  8 – 16

Contents

pp.：  12 – 8

Chapter 0. PRELIMINARY RESULTS

pp.：  16 – 38

Chapter 1. APPROXIMATION OF SMOOTH FUNCTIONS ON MANIFOLDS

pp.：  38 – 68

Chapter 2. SIMULTANEOUS APPROXIMATION OF SMOOTH FUNCTIONS

pp.：  68 – 80

Chapter 3. POLYNOMIAL APPROXIMATION OF DIFFERENTIABLE FUNCTIONS

pp.：  80 – 94

Chapter 4. WEAKLY CONTINUOUS FUNCTIONS ON BANACH SPACES

pp.：  94 – 130

Chapter 5. APPROXIMATION OF WEAKLY UNIFORMLY DIFFERENTIABLE FUNCTIONS

pp.：  130 – 142

Chapter 6. APPROXIMATION FOR THE COMPACT-OPEN TOPOLOGY

pp.：  142 – 148

Chapter 7. APPROXIMATION OF WEAKLY DIFFERENTIABLE FUNCTIONS

pp.：  148 – 166

Chapter 8. SPACES OF DIFFERENTIABLE FUNCTIONS AND THE APPROXIMATION PROPERTY

pp.：  166 – 176

Chapter 9. POLYNOMIAL ALGEBRAS OF CONTINUOUSLY DIFFERENTIABLE FUNCTIONS

pp.：  176 – 184

Chapter 10. ON THE CLOSURE OF MODULES OF CONTINUOUSLY DIFFERENTIABLE FUNCTIONS

pp.：  184 – 192

Chapter 11. HOMOMORPHISMS BETWEEN ALGEBRAS OF UNIFORMLY WEAKLY DIFFERENTIABLE FUNCTIONS

pp.：  192 – 210

Chapter 12. THE PALEY-WIENER -SCHWARTZ THEOREM IN INFINITE DIMENSION

pp.：  210 – 224

Appendix I . WHITNEY'S SPECTRAL THEOREM

pp.：  224 – 236

REFERENCES

pp.：  236 – 250

INDEX

pp.：  250 – 254

INDEX OF SYMBOLS

pp.：  254 – 258

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