Applied Functional Analysis

Description

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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