Description

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. Key Features - 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.

Key Features

· 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.

Readership

Graduate and prost-graduate students, researchers, teachers and professors.

Table of Contents

Preface. Acknowledgements. Contents. 1. Banach Spaces 1.1 Introduction 1.2 Vector Spaces 1.3 Normed Vector Spaces 1.4 Banach Spaces 1.5 Hilbert Space Problems 2. 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 3. 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 4. 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 5. 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 6. The Adjoint Operator 6.1 Introduction 6.2 The Dual of a Banach

Details

No. of pages:
432
Language:
English
Copyright:
© 2005
Published:
Imprint:
Elsevier Science
Electronic ISBN:
9780080527314
Print ISBN:
9780444517906
Print ISBN:
9780444550392

About the authors