应用泛函分析(第2卷)(英文版)
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作者(德)泽德勒|责编:刘慧//高蓉
出版社世界图书出版公司
ISBN9787510005459
出版时间2009-10
装帧其他
开本其他
定价89元
货号30934955
上书时间2024-10-14
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目录
Preface
Contents of AMS Volume 108
1 The Hahn-Banach Theorem and Optimization Problems
1.1 The Hahn-Banach Theorem
1.2 Applications to the Separation of Convex Sets
1.3 The Dual Space C[a,b]*
1.4 Applications to the Moment Problem
1.5 Minimum Norm Problems and Duality Theory
1.6 Applications to Cebysev Approximation
1.7 Applications to the Optimal Control of Rockets
2 Variational Principles and Weak Convergence
2.1 The nth Variation
2.2 Necessary and Suficient Conditions for Local Extrema and the Classical Calculus of Variations
2.3 The Lack of Compactness in Infinite-Dimensional Banach Spaces
2.4 Weak Convergence
2.5 The Generalized Weierstrass Existence Theorem
2.6 Applications to the Calculus of Variations
2.7 Applications to Nonlinear Eigenvalue Problems
2.8 Reflexive Banach Spaces
2.9 Applications to Convex Minimum Problems and Variational Inequalities
2.10 Applications to Obstacle Problems in Elasticity
2.11 Saddle Points
2.12 Applications to Duality Theory
2.13 The von Neumann Minimax Theorem on the Existence of Saddle Points
2.14 Applications to Game Theory
2.15 The Ekeland Principle about Quasi-Minimal Points
2.16 Applications to a General Minimum Principle via the Palais-Smale Condition
2.17 Applications to the Mountain Pass Theorem
2.18 The Galerkin Method and Nonlinear Monotone Operators
2.19 Symmetries and Conservation Laws(The Noether Theorem)
2.20 The Basic Ideas of Gauge Field Theory
2.21 Representations of Lie Algebras
2.22 Applications to Elementary Particles
3 Principles of Linear Functional Analysis
3.1 The Baire Theorem
3.2 Application to the Existence of Nondifferentiable Continuous Functions
3.3 The Uniform Boundedness Theorem
3.4 Applications to Cubature Formulas
3.5 The Open Mapping Theorem
3.6 Product Spaces
3.7 The Closed Graph Theorem
3.8 Applications to Factor Spaces
3.9 Applications to Direct Sums and Projections
3.10 Dual Operators
3.11 The Exactness of the Duality Functor
3.12 Applications to the Closed Range Theorem and to Fredholm Alternatives
4 The Implicit Function Theorem
4.1 m-Linear Bounded Operators
4.2 The Differential of Operators and the Frechet Derivative
4.3 Applications to Analytic Operators
4.4 Integration
4.5 Applications to the Taylor Theorem
4.6 Iterated Derivatives
4.7 The Chain Rule
4.8 The Implicit Function Theorem
4.9 Applications to Diferential Equations
4.10 Diffeomorphisms and the Local Inverse Mapping Theorem
4.11 Equivalent Maps and the Linearization Principle
4.12 The Local Normal Form for Nonlinear Double Spliting Maps
4.13 The Surjective Implicit Function Theorem
4.14 Applications to the Lagrange Multiplier Rule
5 Fredholm Operators
5.1 Duality for Linear Compact Operators
5.2 The Riesz-Schauder Theory on Hilbert Spaces
5.3 Applications to Integral Equations
5.4 Linear Fredholm Operators
5.5 The Riesz-Schauder Theory on Banach Spaces
5.6 Applications to the Spectrum of Linear Compact Operators
5.7 The Parametrix
5.8 Applications to the Perturbation of Fredholm Operators
5.9 Applications to the Product Index Theorem
5.10 Fredholm Alternatives via Dual Pairs
5.11 Applications to Integral Equations and Boundary-Value Problems
5.12 Bifurcation Theory
5.13 Applications to Nonlinear Integral Equations
5.14 Applications to Nonlinear Boundary-Value Problems
5.15 Nonlinear Fredholm Operators
5.16 Interpolation Inequalities
5.17 Applications to the Navier-Stokes Equations
References
Subject Index
内容摘要
本书是一套2卷集的教科书，本书主要面向大学高年级本科书和低年级研究生。
具备本科数学水平就可以读，应用都是从最简单情形入手，应用领域的读者也可以读；全书材料自足，各部分又尽可能保持独立等特点。
本书为《应用泛函分析》第2卷，包含五章内容。
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