| PrefaceContents of AMS Volume 1081 The Hahn-Banach Theorem Optimization Problems1.1 The Hahn-Banach Theorem1.2 Applications to the Separation of Convex Sets1.3 The Dual Space C[a, b]* 1.4 Applications to the Moment Problem1.5 Minimum Norm Problems and Duality Theory1.6 Applications to Cebysev Approximation1.7 Applications to the Optimal Control of Rockets2 Variational Principles and Weak Convergence2.1 The nth Variation2.2 Necessary and Sufficient Conditions for Local Extrema and the Classical Calculus of Variations2.3 The Lack of Compactness in Infinite-Dimensional Banach Spaces2.4 Weak Convergence2.5 The Generalized Weierstrass Existence Theorem2.6 Applications to the Calculus of Variations2.7 Applications to Nonlinear Eigenvalue Problems2.8 Reflexive Banach Spaces2.9 Applications to Convex Minimum Problems and Variational Inequalities2.10 Applications to Obstacle Problems in Elasticity2.11 Saddle Points2.12 Applications to Dui~lity Theory2.13 The von Neumann Minimax Theorem on the Existence of Saddle Points2.14 Applications to Game Theory2.15 The Ekeland Principle about Quasi-Minimal Points2.16 Applications to a General Minimum Principle via the Palais-Smale Condition2.17 Applications to the Mountain Pass Theorem2.18 The Galerkin Men'hod and Nonlinear Monotone Operators2.19 Symmetries and Conservation Laws (The Noether Theorem2.20 The Basic Ideas of Gauge Field Theory2.21 Representations of Lie Algebras2.22 Applications to Elementary Particles3 Principles of Linear Functional Analysis3.1 The Baire Theorem3.2 Application to the Existence of Nondifferentiable Continuous Functions3.3 The Uniform Boundedness Theorem3.4 Applications to Cubature Formulas 3.5 The Open Mapping Theorem3.6 Product Spaces3.7 The Closed Graph Theorem3.8 Applications to Factor Spaces3.9 Applications to Direct Sums and Projections3.10 Dual Operators3.11 The Exactness of the Duality Functor3.12 Applications to the Closed Range Theorem and to Fredholm Alternatives4 The Implicit Function Theorem4.1 m-Linear Bounded Operators4.2 The Differential of Operators and the Fr~chet Derivative4.3 Applications to Analytic Operators4.4 Integration4.5 Applications to the Taylor Theorem4.6 Iterated Derivatives4.7 The Chain Rule4.8 The Implicit Function Theorem4.9 Applications to Differential Equations4.10 Diffeomorphisms and the Local Inverse Mapping Theorem 4.11 Equivalent Maps and the Linearization Principle4.12 The Local Normal Form for Nonlinear Double Splitting Maps4.13 The Surjective Implicit Function Theorem4.14 Applications to the Lagrange Multiplier Rule5 Fredholm Operators5.1 Duality for Linear Compact Operators5.2 The Riesz-Schauder Theory on Hilbert Spaces5.3 Applications to Integral Equations5.4 Linear Fredholm Operators5.5 The Riesz-Schauder Theory on Banach Spaces5.6 Applications to the Spectrum of Linear Compact Operators5.7 The Parametrix5.8 Applications to the Perturbation of Fredholm Operators5.9 Applications to the Product Index Theorem5.10 Fredholm Alternatives via Dual Pairs5.11 Applications to Integral Equations and Boundary-Value Problems5.12 Bifurcation Theory5.13 Applications to Nonlinear Integral Equations5.14 Applications to Nonlinear Boundary-Value Problems 5.15 Nonlinear Fredholm Operators5.16 Interpolation Inequalities5.17 Applications to the Navier-Stokes Equations ReferencesList of SymbolsList of TheoremsList of Most Important DefinitionsSubject Index |
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