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Michael W. Frazier
 出版情報: New York ; Tokyo : Springer, c1999  xvi, 501 p. ; 25 cm シリーズ名: Undergraduate texts in mathematics 所蔵情報: loading…

 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
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Philip E. Gill, Walter Murray, Margaret H. Wright