Contents
Introduction. Notation 1
Chapter 1. A Class of Function Spaces 5
1.1. Definitions and Basic Properties 5
1.2. Some Lemmas 16
1.3. Proof of Theorem 1.1.14 24
1.4. Some Lemmas on Orthogonalization 29
1.5. Proof of Theorem 1.1.15 33
1.6. Homogeneous Spaces 37
1.7. Proof of Theorem 1.6.12 43
1.8. Proof of Theorem 1.6.11 44
Chapter 2. Differentiability and Spectral Synthesis 47
2.1. Capacities and Differentials 47
2.2. Spectral Synthesis 52
2.3. Spectral Synthesis in Spaces of Distributions 57
2.4. Invariant Subspaces and a Theorem of Whitney 64
Chapter 3. Luzin Type Theorems 67
3.1. Luzin Approximation of Functions 67
3.2. Luzin Approximation of Distributions 77
Appendix. Whitney's Approximation Theorem in
Lp(HN),
p 0 87
Bibliography 95
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