| 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 |
図書
