现代数学物理方法（第1卷）

出版时间：2003-6  出版社：M.Reed、 B.Simon 世界图书出版公司 (2003-06出版)  作者：M.Reed，B.Simon 编  页数：400  
Tag标签：无  

内容概要

　　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.

书籍目录

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

编辑推荐

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.

用户评论 (总计3条)

•   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