| Preface | |
| Acknowledgements | |
| Banach Spaces | |
| Introduction | |
| Vector Spaces | |
| Normed Vector Spaces | |
| Banach Spaces | |
| Hilbert Space Problems | |
| Lebesgue Integration and the Lp Spaces | |
| Introduction | |
| The Measure of a Set | |
| Measurable Functions | |
| Integration | |
| The Lp Spaces | |
| Applications Problems | |
| Foundations of Linear Operator Theory | |
| Introduction | |
| The Basic Terminology of Operator Theory | |
| Some Algebraic Properties of Linear Operators | |
| Continuity and Boundedness | |
| Some Fundamental Properties of Bounded Operators | |
| First Results on the Solution of the Equation Lf=g | |
| Introduction to Spectral Theory | |
| Closed Operators and Differential Equations Problems | |
| Introduction to Nonlinear Operators | |
| Introduction | |
| Preliminaries | |
| The Contraction Mapping Principle | |
| The Frechet Derivative | |
| Newton's Method for Nonlinear Operators Problems | |
| Compact Sets in Banach Spaces | |
| Introduction | |
| Definitions | |
| Some Consequences of Compactness | |
| Some Important Compact Sets of Functions Problems | |
| The Adjoint Operator | |
| Introduction | |
| The Dual of a Banach Space | |
| Weak Convergence | |
| Hilbert Space | |
| The Adjoint of a Bounded Linear Operator | |
| Bounded Self-adjoint Operators -- Spectral Theory | |
| The Adjoint of an Unbounded Linear Operator in Hilbert Space Problems | |
| Linear Compact Operators | |
| Introduction | |
| Examples of Compact Operators | |
| The Fredholm Alternative | |
| The Spectrum | |
| Compact Self-adjoint Operators | |
| The Numerical Solution of Linear Integral Equations Problems | |
| Nonlinear Compact Operators and Monotonicity | |
| Introduction | |
| The Schauder Fixed Point Theorem | |
| Positive and Monotone Operators in Partially Ordered Banach Spaces Problems | |
| The Spectral Theorem | |
| Introduction | |
| Preliminaries | |
| Background to the Spectral Theorem | |
| The Spectral Theorem for Bounded Self-adjoint Operators | |
| The Spectrum and the Resolvent | |
| Unbounded Self-adjoint Operators | |
| The Solution of an Evolution Equation Problems | |
| Generalized Eigenfunction Expansions Associated with Ordinary Differential Equations | |
| Introduction | |
| Extensions of Symmetric Operators | |
| Formal Ordinary Differential Operators: Preliminaries | |
| Symmetric Operators Associated with Formal Ordinary Differential Operators | |
| The Construction of Self-adjoint Extensions | |
| Generalized Eigenfunction Expansions Problems | |
| Linear Elliptic Partial Differential Equations | |
| Introduction | |
| Notation | |
| Weak Derivatives and Sobolev Spaces | |
| The Generalized Dirichlet Problem | |
| Fredholm Alternative for Generalized Dirichlet Problem | |
| Smoothness of Weak Solutions | |
| Further Developments Problems | |
| The Finite Element Method | |
| Introduction | |
| The Ritz Method | |
| The Rate of Convergence of the Finite Element Method Problems | |
| Introduction to Degree Theory | |
| Introduction | |
| The Degree in Finite Dimensions | |
| The Leray-Schauder Degree | |
| A Problem in Radiative Transfer Problems | |
| Bifurcation Theory | |
| Introduction | |
| Local Bifurcation Theory | |
| Global Eigenfunction Theory Problems | |
| References | |
| List of Symbols | |
| Index | |
| Table of Contents provided by Publisher. All Rights Reserved. |
