现代数学物理方法（第1卷）
2003-6
M.Reed、 B.Simon 世界图书出版公司 (2003-06出版)
M.Reed，B.Simon 编
400
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This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modem mathematical physics. It describes the fundamental principles of functional analysis and is essentially self-contained, although there are occasional references to later volumes. We have included a few applications when we thought that they would provide motivation for the reader. Later volumes describe various advanced topics in functional analysis and give numerous applications in classical physics, modem physics, and partial differenrial equations.
Preface Introduction Contents of Other Volumes I: PRELIMINARIES 1. Sets and functions 2. Metric and normed linear spaces Appendix Lira sup and lim inf 3. The Lebesgue integral 4. Abstract measure theory 5. Two conrergence arguments 6. Equicontinuity Notes Problems II: HILBERT SPACES 1. The geometry of Hilbert space 2. The Riesz lemma 3. Orthonormal bases 4. Tensor products of Hilbert spaces 5. Ergodic theory: an introduction Notes ProblemsIII: BANACH SPACES 1. Definition and examples 2. Duals and double duals 3. The Hahn-Banach theorem 4. Operations on Banach spaces 5. The Baire category theorem and its consequences Notes ProblemsIV: TOPOLOGICAL SPACES 1. General notions 2. Nets and Convergence 3. Compactness Appendix The Stone-Weierstrass theorem 4. Measure theory on Compact spaces 5. Weak topologies on Banach spaces Appendix Weak and strong measurability Notes ProblemsV: LOCALLY ONVEX SPACES 1. General properties 2. Frdchet spaces 3. Functions of rapid decease and the tempered distributions Appendix The N-representation for and 4. Inductive limits: generalized functions and weak solutions of partial differential equations 5. Fixed point theorems 6. Applications of fixed point theorems 7. Topologies on locally convex spaces: duality theory and the strong dual topology Appendix Polars and the Mackey-Arens theorem Notes ProblemsVI: BOUNDED OPERATORSVII: THE SPECTRAL THEOREMVIII: UNBOUNDED OPERATORSTHE FOURIER TRANSFORMSUPPLEMENTARY MATERIALList of Symbols
This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modem mathematical physics. It describes the fundamental principles of functional analysis and is essentially self-contained, although there are occasional references to later volumes. We have included a few applications when we thought that they would provide motivation for the reader. Later volumes describe various advanced topics in functional analysis and give numerous applications in classical physics, modem physics, and partial differenrial equations.
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和中国大学物理类专业的《数学物理方法》讲述的内容根本不同，无论从广度和深度来说都高太多了。不过很多东西对于搞理论物理和等离子物理这些东西的人来说，还是很必要的。
这部四卷本的数学物理名著写于1978年，作者之一simons是普林斯顿大学的教授，作者将泛函分析在物理学中的应用做了系统的总结。前两卷论述基本理论，很多习题出的非常好。第三卷是讲散射理论，涉及量子力学和量子场论的一些内容。最后一卷讲谱理论。如果能全读下来将受益匪浅。
作为理论物理是一本很好的工具书，只不过内容讲得不够详细