An introduction to wavelets through linear algebra

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An introduction to wavelets through linear algebra / Michael W. Frazier

資料種別:: 図書
出版情報:: New York ; Tokyo : Springer, c1999
形態:: xvi, 501 p. ; 25 cm
シリーズ名:: Undergraduate texts in mathematics <BA00018418>
著者名:: Frazier, Michael, 1956- <DA05742928>
ISBN:: 9780387986395 [0387986391]
書誌ID:: BA4247693X

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注記:

Bibliography: p. 484-490
Includes index

主題:

Algebras, Linear; Wavelets (Mathematics)

言語:

英語

目次情報:

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

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：

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