UID:
almatuudk_9922020400802884
Format:
1 online resource (257 p.)
ISBN:
1-281-79792-8
,
9786611797928
,
0-08-087241-7
Series Statement:
North-Holland mathematics studies ; 130
Content:
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.
Note:
Includes index.
,
Front Cover; Approximation of Continuously Differentiable Functions; Copyright Page; Contents; Foreword; Chapter 0. PRELIMINARY RESULTS; 0.1 Functions on locally compact spaces; 0.2 Whitney's theorems; 0.3 Multilinear mappings and polynomials; 0.4 Polynomials algebras; 0.5 e-product and the approximation property; 0.6 Angelic spaces; 0.7 Absolutely summing operators; 0.8 Real compact spaces; 0.9 Holomorphic functions; 0.10 Weakly compactly generated spaces; 0.11 Injective spaces; 0.12 Some additional theorems; Chapter 1. APPROXIMATION OF SMOOTH FUNCTIONS ON MANIFOLDS; 1.1 Weierstrass' theorem
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1.2 Nachbin's theorem1.3 m-admissible algebras; 1.4 Nachbin m-algebras; 1.5 Modules on strongly separating algebras; 1.6 Dense polynomial algebras; 1.7 Pointwise description of closures; 1.8 Notes, remarks and references; Chapter 2. SIMULTANEOUS APPROXIMATION OF SMOOTH FUNCTIONS; 2.1 Approximation for the fine topology of order m; 2.2 A nonlinear characterization of superreflexive Banach spaces; 2.3 Notes and remarks; Chapter 3. POLYNOMIAL APPROXIMATION OF DIFFERENTIABLE FUNCTIONS; 3.0 Introduction; 3.1 Approximation for the compact-compact topology of order m . Basic density properties
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3.2 Quasi - differentiable functions on Banach spaces . Basic topological properties3.3 On completion of (Pf(E; F); tmc); 3.4 Notes and references; Chapter 4. WEAKLY CONTINUOUS FUNCTIONS ON BANACH SPACES; 4.1 Introduction . Preliminary Definitions . Elementary Properties; 4.2 The bw and bw* topologies; 4.3 Weakly continuous and weakly uniformly continuous functions on bounded sets; 4.4 On completion of spaces of weakly continuous functions; 4.5 Polynomial case; 4.6 Composition of weakly uniformly continuous functions; 4.7 Notes and references
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Chapter 5. APPROXIMATION OF WEAKLY UNIFORMLY DIFFERENTIABLE FUNCTIONS5.1 Introduction; 5.2 Uniformly differentiable functions on bounded sets; 5.3 Extension of Bernstein's theorem to infinite dimensional Banach spaces; 5.4 Notes and references; Chapter 6. APPROXIMATION FOR THE COMPACT-OPEN TOPOLOGY; 6.1 Extension of Weierstrass' theorem for infinite dimensional Banach spaces; 6.2 References; Chapter 7. APPROXIMATION OF WEAKLY DIFFERENTIABLE FUNCTIONS; 7.1 Weakly differentiable functions . Some results on weak compactness . Locally convex structure; 7.2 The bounded weak approximation property
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7.3 Polynomial approximation of weakly differentiable functions7.4 Notes. remarks and references; Chapter 8. SPACES OF DIFFERENTIABLE FUNCTIONS AND THE APPROXIMATION PROPERTY; 8.1 e-products of continuously differentiable function spaces . Applications; 8.2 On the approximation property in :paces of continuously differentiable functions; 8.3 Notes and references; Chapter 9. POLYNOMIAL ALGEBRAS OF CONTINUOUSLY DIFFERENTIABLE FUNCTIONS; 9.1 Polynomial algebras . Extension of Nachbin's theorem to infinite dimensioneal Banach spaces; 9.2 Notes, remarks and references
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Chapter 10. ON THE CLOSURE OF MODULES OF CONTINUOUSLY DIFFERENTIABLE FUNCTIONS
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English
Additional Edition:
ISBN 0-444-70128-1
Language:
English
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