Preface. Acknowledgements. Contents.
1.1 Introduction 1.2 Vector Spaces 1.3 Normed Vector Spaces 1.4 Banach Spaces 1.5 Hilbert Space Problems
Lebesgue Integration and the Lp Spaces
2.1 Introduction 2.2 The Measure of a Set 2.3 Measurable Functions 2.4 Integration 2.5 The Lp Spaces 2.6 Applications Problems
Foundations of Linear Operator Theory
3.1 Introduction 3.2 The Basic Terminology of Operator Theory 3.3 Some Algebraic Properties of Linear Operators 3.4 Continuity and Boundedness 3.5 Some Fundamental Properties of Bounded Operators 3.6 First Results on the Solution of the Equation Lf=g 3.7 Introduction to Spectral Theory 3.8 Closed Operators and Differential Equations Problems
Introduction to Nonlinear Operators
4.1 Introduction 4.2 Preliminaries 4.3 The Contraction Mapping Principle 4.4 The Frechet Derivative 4.5 Newton's Method for Nonlinear Operators Problems
Compact Sets in Banach Spaces
5.1 Introduction 5.2 Definitions 5.3 Some Consequences of Compactness 5.4 Some Important Compact Sets of Functions Problems
The Adjoint Operator
6.1 Introduction 6.2 The Dual of a Banach
Functional analysis is a powerful tool when applied to mathematical problems arising from physical situations. The present book provides, by careful selection of material, a collection of concepts and techniques essential for the modern practitioner. Emphasis is placed on the solution of equations (including nonlinear and partial differential equations). The assumed background is limited to elementary real variable theory and finite-dimensional vector spaces.
- Provides an ideal transition between introductory math courses and advanced graduate study in applied mathematics, the physical sciences, or engineering.
- Gives the reader a keen understanding of applied functional analysis, building progressively from simple background material to the deepest and most significant results.
- Introduces each new topic with a clear, concise explanation.
- Includes numerous examples linking fundamental principles with applications.
- Solidifies the reader’s understanding with numerous end-of-chapter problems.
· Provides an ideal transition between introductory math courses and advanced graduate study in applied mathematics, the physical sciences, or engineering. · Gives the reader a keen understanding of applied functional analysis, building progressively from simple background material to the deepest and most significant results. · Introduces each new topic with a clear, concise explanation. · Includes numerous examples linking fundamental principles with applications. · Solidifies the reader's understanding with numerous end-of-chapter problems.
Graduate and prost-graduate students, researchers, teachers and professors.
- No. of pages:
- © Elsevier Science 2005
- 8th February 2005
- Elsevier Science
- eBook ISBN:
- Hardcover ISBN:
University of Sheffield, UK
University of Sheffield, UK
Lawrence Technological University, Southfield, USA