Applied functional analysis : numerical methods, wavelet methods, and image processing

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Applied functional analysis : numerical methods, wavelet methods, and image processing / Abul Hasan Siddiqi

資料種別:: 図書
出版情報:: New York : Marcel Dekker, c2004
形態:: xviii, 575 p. ; 24 cm
シリーズ名:: Monographs and textbooks in pure and applied mathematics ; 258 <BA00046446>
著者名:: Siddiqi, Abul Hasan
ISBN:: 9780824740979 [0824740971]
書誌ID:: BA64263830

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注記:

Includes bibliographical references and index

言語:

英語

目次情報:

Preface

List of Figures

Metric Spaces and Banach Fixed Point Theorem / 1：

Introduction / 1.1：

Banach Contraction Fixed Point Theorem / 1.2：

Application of Banach Contraction Mapping Theorem / 1.3：

Application to Real-valued Equation / 1.3.1：

Application to Matrix Equation / 1.3.2：

Application to Integral Equation / 1.3.3：

Application to Differential Equation / 1.3.4：

Problems / 1.4：

References

Banach Spaces / 2：

Definitions and Examples of Normed and Banach Spaces / 2.1：

Examples of Normed and Banach Spaces / 2.2.1：

Basic Properties--Closure, Denseness and Separability / 2.3：

Closed, Dense and Separable Sets / 2.3.1：

Riesz Theorem and Construction of a New Banach Space / 2.3.2：

Dimension of Normed Spaces / 2.3.3：

Open and Closed Spheres / 2.3.4：

Bounded and Unbounded Operators / 2.4：

Definitions and Examples / 2.4.1：

Properties of Linear Operators / 2.4.2：

Unbounded Operators / 2.4.3：

Representation of Bounded and Linear Functionals / 2.5：

Algebra of Operators / 2.6：

Convex Functionals / 2.7：

Convex Sets / 2.7.1：

Affine Operator / 2.7.2：

Lower Semicontinuous and Upper Semicontinuous Functionals / 2.7.3：

Solved Problems / 2.8：

Unsolved Problems / 2.8.2：

Hilbert Space / 3：

Basic Definition and Properties / 3.1：

Definitions, Examples and Properties of Inner Product Space / 3.2.1：

Parallelogram Law and Characterization of Hilbert Space / 3.2.2：

Orthogonal Complements and Projection Theorem / 3.3：

Orthogonal Complements and Projections / 3.3.1：

Orthogonal Projections and Projection Theorem / 3.4：

Projection on Convex Sets / 3.5：

Orthonormal Systems and Fourier Expansion / 3.6：

Duality and Reflexivity / 3.7：

Riesz Representation Theorem / 3.7.1：

Reflexivity of Hilbert Spaces / 3.7.2：

Operators in Hilbert Space / 3.8：

Adjoint of Bounded Linear Operators on a Hilbert Space / 3.8.1：

Self-Adjoint, Positive, Normal and Unitary Operators / 3.8.2：

Adjoint of an Unbounded Linear Operator / 3.8.3：

Bilinear Forms and Lax-Milgram Lemma / 3.9：

Basic Properties / 3.9.1：

Fundamental Theorems / 3.10：

Hahn-Banach Theorem / 4.1：

Extension Form of Hahn-Banach Theorem / 4.2.1：

Extension Form of the Hahn-Banach Theorem / 4.2.2：

Topologies on Normed Spaces / 4.3：

Strong and Weak Topologies / 4.3.1：

Weak Convergence / 4.4：

Weak Convergence in Banach Spaces / 4.4.1：

Weak Convergence in Hilbert Spaces / 4.4.2：

Banach-Alaoglu Theorem / 4.5：

Principle of Uniform Boundedness and Its Applications / 4.6：

Principle of Uniform Boundedness / 4.6.1：

Open Mapping and Closed Graph Theorems / 4.7：

Graph of a Linear Operator and Closedness Property / 4.7.1：

Open Mapping Theorem / 4.7.2：

The Closed-Graph Theorem / 4.7.3：

Differential and Integral Calculus in Banach Spaces / 4.8：

The Gateaux and Frechet Derivatives / 5.1：

The Gateaux Derivative / 5.2.1：

The Frechet Derivative / 5.2.2：

Generalized Gradient (Subdifferential) / 5.3：

Some Basic Results from Distribution Theory and Sobolev Spaces / 5.4：

Distributions / 5.4.1：

Sobolev Space / 5.4.2：

The Sobolev Embedding Theorems / 5.4.3：

Integration in Banach Spaces / 5.5：

Optimization Problems / 5.6：

General Results on Optimization / 6.1：

Special Classes of Optimization Problems / 6.3：

Convex, Quadratic and Linear Programming / 6.3.1：

Calculus of Variations and Euler-Lagrange Equation / 6.3.2：

Minimization of Energy Functional (Quadratic Functional) / 6.3.3：

Algorithmic Optimization / 6.4：

Newton Algorithm and Its Generalization / 6.4.1：

Conjugate Gradient Method / 6.4.2：

Operator Equations and Variational Methods / 6.5：

Boundary Value Problems / 7.1：

Operator Equations and Solvability Conditions / 7.3：

Equivalence of Operator Equation and Minimization Problem / 7.3.1：

Solvability Conditions / 7.3.2：

Existence Theorem for Nonlinear Operators / 7.3.3：

Existence of Solutions of Dirichlet and Neumann Boundary Value Problems / 7.4：

Approximation Method for Operator Equations / 7.5：

Galerkin Method / 7.5.1：

Rayleigh-Ritz-Galerkin Method / 7.5.2：

Eigenvalue Problems / 7.6：

Eigenvalue of Bilinear Form / 7.6.1：

Existence and Uniqueness / 7.6.2：

Boundary Value Problems in Science and Technology / 7.7：

Finite Element and Boundary Element Methods / 7.8：

Finite Element Method / 8.1：

Abstract Problem and Error Estimation / 8.2.1：

Internal Approximation of H[superscript 1] ([Omega]) / 8.2.2：

Finite Elements / 8.2.3：

Applications of the Finite Method in Solving Boundary Value Problems / 8.3：

Basic Ingredients of Boundary Element Method / 8.4：

Weighted Residuals Method / 8.4.1：

Inverse Problem and Boundary Solutions / 8.4.2：

Boundary Element Method / 8.4.3：

Variational Inequalities and Applications / 8.5：

Motivation and Historical Remarks / 9.1：

Contact Problem (Signorini Problem) / 9.1.1：

Variational Inequalities in Social, Financial and Management Sciences / 9.1.2：

Variational Inequalities and Their Relationship with Other Problems / 9.2：

Classes of Variational Inequalities / 9.2.1：

Formulation of a Few Problems in Terms of Variational Inequalities / 9.2.2：

Elliptic Variational Inequalities / 9.3：

Lions-Stampacchia Theorem / 9.3.1：

Variational Inequalities for Monotone Operators / 9.3.2：

Finite Element Methods for Variational Inequalities / 9.4：

Convergence and Error Estimation / 9.4.1：

Error Estimation in Concrete Cases / 9.4.2：

Evolution Variational Inequalities and Parallel Algorithms / 9.5：

Solution of Evolution Variational Inequalities / 9.5.1：

Decomposition Method and Parallel Algorithms / 9.5.2：

Obstacle Problem / 9.6：

Membrane Problem / 9.6.1：

Wavelet Theory / 9.7：

Continuous and Discrete Wavelet Transforms / 10.1：

Continuous Wavelet Transforms / 10.2.1：

Discrete Wavelet Transform and Wavelet Series / 10.2.2：

Multiresolution Analysis, Wavelets Decomposition and Reconstruction / 10.3：

Multiresolution Analysis (MRA) / 10.3.1：

Decomposition and Reconstruction Algorithms / 10.3.2：

Connection with Signal Processing / 10.3.3：

The Fast Wavelet Transform Algorithm / 10.3.4：

Wavelets and Smoothness of Functions / 10.4：

Lipschitz Class and Wavelets / 10.4.1：

Approximation and Detail Operators / 10.4.2：

Scaling and Wavelet Filters / 10.4.3：

Approximation by MRA Associated Projections / 10.4.4：

Compactly Supported Wavelets / 10.5：

Daubechies Wavelets / 10.5.1：

Approximation by Family of Daubechies Wavelets / 10.5.2：

Wavelet Packets / 10.6：

Wavelet Method for Partial Differential Equations and Image Processing / 10.7：

Wavelet Methods in Partial Differential and Integral Equations / 11.1：

General Procedure / 11.2.1：

Miscellaneous Examples / 11.2.3：

Error Estimation Using Wavelet Basis / 11.2.4：

Introduction to Signal and Image Processing / 11.3：

Representation of Signals by Frames / 11.4：

Functional Analytic Formulation / 11.4.1：

Iterative Reconstruction / 11.4.2：

Noise Removal from Signals / 11.5：

Model and Algorithm / 11.5.1：

Wavelet Methods for Image Processing / 11.6：

Besov Space / 11.6.1：

Linear and Nonlinear Image Compression / 11.6.2：

Appendices / 11.7：

Set Theoretic Concepts / A：

Topological Concepts / B：

Elements of Metric Spaces / C：

Notations and Definitions of Concrete Spaces / D：

Vector Spaces / E：

Fourier Analysis / F：

Symbols and Abbreviations

Index

Preface

List of Figures

Metric Spaces and Banach Fixed Point Theorem / 1：

Introduction / 1.1：

Banach Contraction Fixed Point Theorem / 1.2：

Application of Banach Contraction Mapping Theorem / 1.3：

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