文件名称：Functional Analysis(泛函权威写的泛函书，英文原版)
文件大小：910KB
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更新时间：2012-08-20 11:24:37
Functional Analysis
Preface v Chapter 0. Introduction 1 x0.1. Linear partial di erential equations 1 Chapter 1. A rst look at Banach and Hilbert spaces 5 x1.1. Warm up: Metric and topological spaces 5 x1.2. The Banach space of continuous functions 14 x1.3. The geometry of Hilbert spaces 19 x1.4. Completeness 24 x1.5. Bounded operators 25 Chapter 2. Hilbert spaces 29 x2.1. Orthonormal bases 29 x2.2. The projection theorem and the Riesz lemma 34 x2.3. Operators de ned via forms 35 x2.4. Orthogonal sums and tensor products 37 Chapter 3. Compact operators 41 x3.1. Compact operators 41 x3.2. The spectral theorem for compact symmetric operators 43 x3.3. Applications to Sturm{Liouville operators 46 x3.4. Fredholm theory for compact operators 49 Chapter 4. Almost everything about Lebesgue integration 55 x4.1. Borel measures in a nut shell 55 x4.2. Measurable functions 64 x4.3. Integration | Sum me up Henri 66 x4.4. Product measures 70 Chapter 5. The Lebesgue spaces Lp 75 x5.1. Functions almost everywhere 75 x5.2. Jensen Holder Minkowski 77 x5.3. Nothing missing in Lp 80 x5.4. Integral operators 83 Chapter 6. The main theorems about Banach spaces 87 x6.1. The Baire theorem and its consequences 87 x6.2. The Hahn{Banach theorem and its consequences 91 x6.3. Weak convergence 97 Chapter 7. The dual of Lp 103 x7.1. Decomposition of measures 103 x7.2. Complex measures 106 x7.3. The dual of Lp, p < 1 109 x7.4. The dual of L1 and the Riesz representation theorem 110 Chapter 8. Bounded linear operators 115 x8.1. Banach algebras 115 x8.2. The C algebra of operators and the spectral theorem 120 x8.3. The Stone{Weierstra theorem 124 Appendix A. Zorn's lemma 127 Bibliography 129 Glossary of notation 131 Index 133