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Preface

Acknowledgments

Prologue: Compression of the FBI Fingerprint Files

Background: Complex Numbers and Linear Algebra / 1：

Real Numbers and Complex Numbers / 1.1：

Complex Series, Euler's Formula, and the Roots of Unity / 1.2：

Vector Spaces and Bases / 1.3：

Linear Transformations, Matrices, and Change of Basis / 1.4：

Diagonalization of Linear Transformations and Matrices / 1.5：

Inner Products, Orthonormal Bases, and Unitary Matrices / 1.6：

The Discrete Fourier Transform / 2：

Basic Properties of the Discrete Fourier Transform / 2.1：

Translation-Invariant Linear Transformations / 2.2：

The Fast Fourier Transform / 2.3：

Wavelets on $bZ_N$ / 3：

Construction of Wavelets on $bZ_N$: The First Stage / 3.1：

Construction of Wavelets on $bZ_N$: The Iteration Step / 3.2：

Examples and Applications / 3.3：

Wavelets on $bZ$ / 4：

$ ell ^2(bZ)$ / 4.1：

Complete Orthonormal Sets in Hilbert Spaces / 4.2：

$L^2([- pi , pi ))$ and Fourier Series / 4.3：

The Fourier Transform and Convolution on $ ell ^2(bZ)$ / 4.4：

First-Stage Wavelets on $bZ$ / 4.5：

The Iteration Step for Wavelets on $bZ$ / 4.6：

Implementation and Examples / 4.7：

Wavelets on $bR$ / 5：

$L^2(bR)$ and Approximate Identities / 5.1：

The Fourier Transform on $bR$ / 5.2：

Multiresolution Analysis and Wavelets / 5.3：

Construction of Multiresolution Analyses / 5.4：

Wavelets with Compact Support and Their Computation / 5.5：

Wavelets and Differential Equations / 6：

The Condition Number of a Matrix / 6.1：

Finite Difference Methods for Differential Equations / 6.2：

Wavelet-Galerkin Methods for Differential Equations / 6.3：

Bibliography

Index

Preface

Acknowledgments

Prologue: Compression of the FBI Fingerprint Files

目次情報: 続きを見る

Fundamentals

Duality

Linear Mappings

Matrices

Determinant and Trace

Spectral Theory

Euclidean Structure

Spectral Theory of Selfadjoint Mappings

Calculus of Vector and Matrix Valued Functions

Matrix Inequalities

Kinematics and Dynamics

Convexity

The Duality Theorem

Normed Linear Spaces

Linear Mappings Between Normed Spaces

Positive Matrices

How to Solve Systems of Linear Equations

Appendices

Bibliography

Index

List of Series Titles

Fundamentals

Duality

Linear Mappings

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