Science/Engineering Applied Functional Analysis (Pure and Applied Mathematics): Abul Hasan Siddiqi (0824740971)

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Applied Functional Analysis (Pure and Applied Mathematics): Abul Hasan Siddiqi

Siddiqi (mathematical sciences, King Fahd University of Petroleum and Minerals, Saudi Arabia) offers a comprehensive treatment of functional analysis results relevant to scientific and technological applications. Introducing recent results in wavelet analysis as applied in partial differential equations and signal and image processing, he covers metric, Banach, and Hilbert spaces, fundamental theorems, optimization problems, finite and boundary element methods, and wavelet theory. Chapter problems are included. Intended as a text for graduate and senior undergraduates in mathematics, the book can also be used for advanced courses in systems engineering, computer engineering, and management sciences.

Table of Contents

Preface

List of Figures

1 Metric Spaces and Banach Fixed Point Theorem 1

2 Banach Spaces 19

3 Hilbert Space 85

4 Fundamental Theorems 167

5 Differential and Integral Calculus in Banach Spaces 201

6 Optimization Problems 257

7 Operator Equations and Variational Methods 283

8 Finite Element and Boundary Element Methods 315

9 Variational Inequalities and Applications 359

10 Wavelet Theory 407

11 Wavelet Method for Partial Differential Equations and Image Processing 485

References 519

App. A Set Theoretic Concepts 523

App. B Topological Concepts 529

App. C Elements of Metric Spaces 533

App. D Notations and Definitions of Concrete Spaces 539

App. E Vector Spaces 551

App. F Fourier Analysis 555

References 563

Symbols and Abbreviations 565

Index 567

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