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1.

図書
図書
1. Wavelet methods for time series analysis
Donald B. Percival, Andrew T. Walden
出版情報: Cambridge : Cambridge University Press, 2000  xxv, 594 p. ; 27 cm
シリーズ名: Cambridge series on statistical and probabilistic mathematics
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目次情報: 続きを見る
Introduction to wavelets / 1：
Review of Fourier theory and filters / 2：
Orthonormal transforms of time series / 3：
The discrete wavelet transform / 4：
The maximal overlap discrete wavelet transform / 5：
The discrete wavelet packet transform / 6：
Random variables and stochastic processes / 7：
The wavelet variance / 8：
Analysis and synthesis of long memory processes / 9：
Wavelet-based signal estimation / 10：
Wavelet analysis of finite energy signals / 11：
Appendix. Answers to embedded exercises
References
Author index
Subject index
Introduction to wavelets / 1：
Review of Fourier theory and filters / 2：
Orthonormal transforms of time series / 3：
2.

図書
図書
2. Complex harmonic splines, periodic quasi-wavelets : theory and applications
by Han-lin Chen
出版情報: Dordrecht ; Boston : Kluwer Academic, c2000  xii, 226 p. ; 25 cm
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3.

図書
図書
3. Fourier and wavelet analysis
George Bachman, Lawrence Narici, Edward Beckenstein
出版情報: New York : Springer, c2000  ix, 505 p. ; 25 cm
シリーズ名: Universitext
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4.

図書
図書
4. An introduction to wavelets through linear algebra
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
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目次情報: 続きを見る
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
5.

図書
図書
5. Wavelets : the key to intermittent information?
edited by B.W. Silverman and J.C. Vassilicos
出版情報: Oxford ; New York : Oxford University Press, c1999,2000  xiv, 256 p., [1] p. of plate ; 24 cm
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目次情報: 続きを見る
Contributors
Wavelets on irregular point sets / Ingrid Daubechies et al.1：
Revealing a lognormal cascading process in turbulent velocity statistics with wavelet analysis / A. Arneodo et al.2：
Wavelets for the study of intermittency and its topology / F. Nicolleau ; J. C. Vassilicos3：
Wavelets in statistics: beyond the standard assumptions / Bernard W. Silverman4：
Wavelets and the theory of non-parametric function estimation / Iain M. Johnstone5：
Ridgelets: a key to higher-dimensional intermittency? / Emmanuel J. Candes ; David L. Donoho6：
Wavelets in time-series analysis / Guy P. Nason ; Rainer von Sachs7：
Wavelets, vision and the statistics of natural scenes / D. J. Field8：
Image processing with complex wavelets / Nick Kingsbury9：
Application of wavelets to filtering of noisy data / Ue-Li Pen10：
Approximation and compression of piecewise smooth functions / Paolo Prandoni ; Martin Vetterli11：
The contribution of wavelets to the analysis of economic and financial data / James B. Ramsey12：
Harmonic wavelets in vibrations and acoustics / D. E. Newland13：
Contributors
Wavelets on irregular point sets / Ingrid Daubechies et al.1：
Revealing a lognormal cascading process in turbulent velocity statistics with wavelet analysis / A. Arneodo et al.2：
6.

図書
図書
6. Wavelets made easy (: Boston ; : Basel)
Yves Nievergelt
出版情報: Boston : Birkhäuser, c1999  xi, 297 p. ; 25 cm
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7.

図書
図書
7. Wavelets, vibrations, and scalings
Yves Meyer
出版情報: Providence, R.I. : American Mathematical Society, c1998  ix, 133 p. ; 27 cm
シリーズ名: CRM monograph series ; v. 9
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8.

図書
図書
8. A wavelet tour of signal processing
Stéphane Mallat
出版情報: San Diego : Academic Press, c1998  xxii, 577 p. ; 24 cm
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9.

図書
図書
9. Multiscale wavelet methods for partial differential equations
edited by Wolfgang Dahmen, Andrew Kurdila, Peter Oswald
出版情報: San Diego : Academic Press, c1997  xiv, 570 p.: ill. ; 24 cm
シリーズ名: Wavelet analysis and its applications ; v. 6
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FEM-Like Multilevel Preconditioning / P. Oswald
Multilevel Solvers for Elliptic Problems on Domains / P. Vassilevski ; J. Wang
Wavelet-Like Methods in the Design of Efficient Multilevel Preconditioners for Elliptic PDEs
Fast Wavelet al.gorithms: Compression and Adaptivity: S. Bertoluzza, An Adaptive Collocation Method Based on Interpolating / Wavelets G. Beylkin ; J. Keiser
An Adaptive Pseudo-Wavelet Approach for Solving Nonlinear Partial Differential Equations / P. Joly ; Y. Maday ; V. Perrier
A Dynamical Adaptive Concept Based on Wavelet Packet Best Bases: Application to Convection Diffusion Partial Differential Equations / S. Dahlke ; W. Dahmen ; R. DeVore
Nonlinear Approximation and Adaptive Techniques for Solving Elliptic Operator Equations
Wavelet Solvers for Integral Equations / T. von Petersdorff ; C. Schwab
Fully Discrete Multiscale Galerkin BEM / A. Rieder
Wavelet Multilevel Solvers for Linear Ill-Posed Problems Stabilized by Tikhonov Regularization
Software Tools and Numerical Experiments / T. Barsch ; A. Kunoth ; K. Urban
Towards Object Oriented Software Tools for Numerical Multiscale Methods for PDEs Using Wavelets / J. Ko ; A. Kurdila
Scaling Function and Wavelet Preconditioners for Second Order Elliptic Problems
Multiscale Interaction and Applications to Turbulence / J. Elezgaray ; G. Berkooz ; H. Dankowicz ; P. Holmes ; M. Myers
Local Models and Large Scale Statistics of the Kuramoto-Sivashinsky Equation / M. Wickerhauser ; M. Farge ; E. Goirand
Theoretical Dimension and the Complexity of Simulated Turbulence
Wavelet Analysis of Partial Differential Operators / J-M. Angeletti ; S. Mazet ; P. Tchamitchian
Analysis of Second-Order Elliptic Operators Without Boundary Conditions and With VMO or Hilderian Coefficients / M. Holschneider
Some Directional Elliptic Regularity for Domains with Cusps
Subject Index
FEM-Like Multilevel Preconditioning / P. Oswald
Multilevel Solvers for Elliptic Problems on Domains / P. Vassilevski ; J. Wang
Wavelet-Like Methods in the Design of Efficient Multilevel Preconditioners for Elliptic PDEs
10.

図書
図書
10. Wavelet theory and harmonic analysis in applied sciences (: hc)
C.E. D'Attellis, E.M. Fernández-Berdaguer, editors
出版情報: Boston, Mass. : Birkhäuser, 1997  xviii, 345 p. ; 24 cm
シリーズ名: Applied and numerical harmonic analysis / series editor, John J. Benedetto
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11.

図書
図書
11. Wavelets : theory and applications
A.K. Louis, P. Maaß, A. Rieder
出版情報: Chichester : Wiley, c1997  xvii, 324 p. ; 24 cm
シリーズ名: Pure and applied mathematics
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The Continuous Wavelets Transform
The Discrete Wavelet Transform
Applications of the Wavelet Transform
Appendix
References
Index
The Continuous Wavelets Transform
The Discrete Wavelet Transform
Applications of the Wavelet Transform
12.

図書
図書
12. The Gibbs phenomenon in Fourier analysis, splines and wavelet approximations
by Abdul J. Jerri
出版情報: Dordrecht ; Boston : Kluwer Academic Publishers, c1998  xxvii, 336 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 446
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13.

図書
図書
13. A mathematical introduction to wavelets (: hbk ; : pbk)
P. Wojtaszczyk
出版情報: Cambridge : Cambridge University Press, 1997  xii, 261 p. ; 23 cm
シリーズ名: London Mathematical Society student texts ; v. 37
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A small sample / 1：
General constructions / 2：
Some important wavelets / 3：
Compactly supported wavelets / 4：
Multivariable wavelets / 5：
Function spaces / 6：
Unconditional convergence / 7：
Wavelet bases in Lp and H1 / 8：
Wavelets and smoothness of functions / 9：
A small sample / 1：
General constructions / 2：
Some important wavelets / 3：
14.

図書
図書
14. Wavelets and subband coding
Martin Vetterli, Jelena Kovačević
出版情報: Englewood Cliffs, N.J. : Prentice Hall PTR, c1995  xvi, 488 p. ; 25 cm
シリーズ名: Prentice Hall signal processing series
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15.

図書
図書
15. Subband and wavelet transforms : design and applications
edited by Ali N. Akansu, Mark J. T. Smith ; foreword by James F. Kaiser
出版情報: Boston : Kluwer Academic Publishers, c1996 [i.e. 1995]  xvi, 451 p. ; 25 cm
シリーズ名: The Kluwer international series in engineering and computer science ; SECS 340
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16.

図書
図書
16. A first course on wavelets
Eugenio Hernández, Guido Weiss
出版情報: Boca Raton ; Tokyo : CRC Press, c1996  489 p. ; 24 cm
シリーズ名: Studies in advanced mathematics
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17.

図書
図書
17. Multidimensional filter banks and wavelets : basic theory and cosine modulated filter banks
edited by Sankar Basu, Bernard Levy
出版情報: Boston, Mass. : Kluwer Academic Publishers, 1996  143 p. ; 25 cm
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目次情報: 続きを見る
Editorial / N.K. Bose
Introduction
Theory and Design of Two-Dimensional Filter Banks: A Review / Yuan-Pei Lin ; P.P. Vaidyanathan
Local Orthogonal Bases I: Construction / R. Bernardini ; J. Kovacevic
Local Orthogonal Bases II: Window Design
Editorial / N.K. Bose
Introduction
Theory and Design of Two-Dimensional Filter Banks: A Review / Yuan-Pei Lin ; P.P. Vaidyanathan
18.

図書
図書
18. An introduction to wavelets (: hbk ; : pbk)
Charles K. Chui
出版情報: Boston ; Tokyo : Academic Press, c1992  x, 266 p. ; 24 cm
シリーズ名: Wavelet analysis and its applications ; v. 1
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An Overview: From Fourier Analysis to Wavelet Analysis
The Integral Wavelet Transform and Time-Frequency Analysis
Inversion Formulas and Duals
Classification of Wavelets
Multiresolution Analysis, Splines, and Wavelets
Wavelet Decompositions and Reconstructions
Fourier Analysis: Fourier and Inverse Fourier Transforms
Continuous-Time Convolution and the Delta Function
Fourier Transform of Square-Integrable Functions
Fourier Series
Basic Convergence Theory and Poisson's Summation Formula
Wavelet Transforms and Time-Frequency Analysis: The Gabor Transform
Short-Time Fourier Transforms and the Uncertainty Principle
The Integral Wavelet Transform
Dyadic Wavelets and Inversions
Frames
Wavelet Series
Cardinal Spline Analysis: Cardinal Spline Spaces
B-Splines and Their Basic Properties
The Two-Scale Relation and an Interpolatory Graphical Display Algorithm
B-Net Representations and Computation of Cardinal Splines
Construction of Spline Approximation Formulas
Construction of Spline Interpolation Formulas
Scaling Functions and Wavelets: Multiresolution Analysis
Scaling Functions with Finite Two-Scale Relations
Direct-Sum Decompositions of L2(R)
Wavelets and Their Duals
Linear-Phase Filtering
Compactly Supported Wavelets
Cardinal Spline-Wavelets: Interpolaratory Spline-Wavelets
Compactly Supported Spline-Wavelets
Computation of Cardinal Spline-Wavelets
Euler-Frobenius Polynomials
Error Analysis in Spline-Wavelet Decomposition
Total Positivity, Complete Oscillation, Zero-Crossings
Orthogonal Wavelets and Wavelet Packets: Examples of Orthogonal Wavelets
Identification of Orthogonal Two-Scale Symbols
Construction of Compactly Supported Orthogonal Wavelets
Orthogonal Wavelet Packets
Orthogonal Decomposition of Wavelet Series
Notes
References
Subject Index
Appendix
An Overview: From Fourier Analysis to Wavelet Analysis
The Integral Wavelet Transform and Time-Frequency Analysis
Inversion Formulas and Duals
19.

図書
図書
19. Wavelet theory and its applications
Randy K. Young
出版情報: Boston : Kluwer Academic Publishers, c1993  xiv, 223 p. ; 25 cm
シリーズ名: The Kluwer international series in engineering and computer science ; SECS 189
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20.

図書
図書
20. Wavelet theory and application
edited by Andrew Laine
出版情報: Boston : Kluwer Academic, c1993  134 p. ; 27 cm
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21.

図書
図書
21. Wavelets : mathematics and applications
[edited by] John J. Benedetto, Michael W. Frazier
出版情報: Boca Raton, Florida ; Tokyo : CRC Press, c1994  575 p. ; 25 cm
シリーズ名: Studies in advanced mathematics
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22.

図書
図書
22. Wavelet basics
by Y.T. Chan
出版情報: Boston : Kluwer Academic Publishers, c1995  134 p. ; 25 cm
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目次情報: 続きを見る
Preface
Introduction / 1：
Principles of the Wavelet Transform / 2：
Multiresolution Analysis, Wavelets and Digital Filters / 3：
Current Topics / 4：
References
Index
Preface
Introduction / 1：
Principles of the Wavelet Transform / 2：
23.

図書
図書
23. Introduction to Fourier analysis and wavelets
Mark A. Pinsky
出版情報: Australia : Brooks/Cole, c2002  xviii, 376 p. ; 25 cm
シリーズ名: Brooks/Cole series in advanced mathematics
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目次情報: 続きを見る
Fourier Series on the Circle / 1：
Motivation and Heuristics / 1.1：
Motivation from Physics / 1.1.1：
The Vibrating String / 1.1.1.1：
Heat Flow in Solids / 1.1.1.2：
Absolutely Convergent Trigonometric Series / 1.1.2：
Examples of Factorial and Bessel Functions / 1.1.3：
Poisson Kernel Example / 1.1.4：
Proof of Laplace's Method / 1.1.5：
Nonabsolutely Convergent Trigonometric Series / 1.1.6：
Formulation of Fourier Series / 1.2：
Fourier Coefficients and Their Basic Properties / 1.2.1：
Fourier Series of Finite Measures / 1.2.2：
Rates of Decay of Fourier Coefficients / 1.2.3：
Piecewise Smooth Functions / 1.2.3.1：
Fourier Characterization of Analytic Functions / 1.2.3.2：
Sine Integral / 1.2.4：
Other Proofs That Si([infinity]) = 1 / 1.2.4.1：
Pointwise Convergence Criteria / 1.2.5：
Integration of Fourier Series / 1.2.6：
Convergence of Fourier Series of Measures / 1.2.6.1：
Riemann Localization Principle / 1.2.7：
Gibbs-Wilbraham Phenomenon / 1.2.8：
The General Case / 1.2.8.1：
Fourier Series in L[superscript 2] / 1.3：
Mean Square Approximation--Parseval's Theorem / 1.3.1：
Application to the Isoperimetric Inequality / 1.3.2：
Rates of Convergence in L[superscript 2] / 1.3.3：
Application to Absolutely-Convergent Fourier Series / 1.3.3.1：
Norm Convergence and Summability / 1.4：
Approximate Identities / 1.4.1：
Almost-Everywhere Convergence of the Abel Means / 1.4.1.1：
Summability Matrices / 1.4.2：
Fejer Means of a Fourier Series / 1.4.3：
Wiener's Closure Theorem on the Circle / 1.4.3.1：
Equidistribution Modulo One / 1.4.4：
Hardy's Tauberian Theorem / 1.4.5：
Improved Trigonometric Approximation / 1.5：
Rates of Convergence in C (T) / 1.5.1：
Approximation with Fejer Means / 1.5.2：
Jackson's Theorem / 1.5.3：
Higher-Order Approximation / 1.5.4：
Converse Theorems of Bernstein / 1.5.5：
Divergence of Fourier Series / 1.6：
The Example of du Bois-Reymond / 1.6.1：
Analysis via Lebesgue Constants / 1.6.2：
Divergence in the Space L[superscript 1] / 1.6.3：
Appendix: Complements on Laplace's Method / 1.7：
First Variation on the Theme-Gaussian Approximation / 1.7.0.1：
Second Variation on the Theme-Improved Error Estimate / 1.7.0.2：
Application to Bessel Functions / 1.7.1：
The Local Limit Theorem of DeMoivre-Laplace / 1.7.2：
Appendix: Proof of the Uniform Boundedness Theorem / 1.8：
Appendix: Higher-Order Bessel functions / 1.9：
Appendix: Cantor's Uniqueness Theorem / 1.10：
Fourier Transforms on the Line And Space / 2：
Basic Properties of the Fourier Transform / 2.1：
Riemann-Lebesgue Lemma / 2.2.1：
Approximate Identities and Gaussian Summability / 2.2.2：
Improved Approximate Identities for Pointwise Convergence / 2.2.2.1：
Application to the Fourier Transform / 2.2.2.2：
The n-Dimensional Poisson Kernel / 2.2.2.3：
Fourier Transforms of Tempered Distributions / 2.2.3：
Characterization of the Gaussian Density / 2.2.4：
Wiener's Density Theorem / 2.2.5：
Fourier Inversion in One Dimension / 2.3：
Dirichlet Kernel and Symmetric Partial Sums / 2.3.1：
Example of the Indicator Function / 2.3.2：
Dini Convergence Theorem / 2.3.3：
Extension to Fourier's Single Integral / 2.3.4.1：
Smoothing Operations in R[superscript 1]-Averaging and Summability / 2.3.5：
Averaging and Weak Convergence / 2.3.6：
Cesaro Summability / 2.3.7：
Approximation Properties of the Fejer Kernel / 2.3.7.1：
Bernstein's Inequality / 2.3.8：
One-Sided Fourier Integral Representation / 2.3.9：
Fourier Cosine Transform / 2.3.9.1：
Fourier Sine Transform / 2.3.9.2：
Generalized h-Transform / 2.3.9.3：
L[superscript 2] Theory in R[superscript n] / 2.4：
Plancherel's Theorem / 2.4.1：
Bernstein's Theorem for Fourier Transforms / 2.4.2：
The Uncertainty Principle / 2.4.3：
Uncertainty Principle on the Circle / 2.4.3.1：
Spectral Analysis of the Fourier Transform / 2.4.4：
Hermite Polynomials / 2.4.4.1：
Eigenfunction of the Fourier Transform / 2.4.4.2：
Orthogonality Properties / 2.4.4.3：
Completeness / 2.4.4.4：
Spherical Fourier Inversion in R[superscript n] / 2.5：
Bochner's Approach / 2.5.1：
Piecewise Smooth Viewpoint / 2.5.2：
Relations with the Wave Equation / 2.5.3：
The Method of Brandolini and Colzani / 2.5.3.1：
Bochner-Riesz Summability / 2.5.4：
A General Theorem on Almost-Everywhere Summability / 2.5.4.1：
Bessel Functions / 2.6：
Fourier Transforms of Radial Functions / 2.6.1：
L[superscript 2]-Restriction Theorems for the Fourier Transform / 2.6.2：
An Improved Result / 2.6.2.1：
Limitations on the Range of p / 2.6.2.2：
The Method of Stationary Phase / 2.7：
Statement of the Result / 2.7.1：
Proof of the Method of Stationary Phase / 2.7.2：
Abel's Lemma / 2.7.4：
Fourier Analysis in L[superscript p] Spaces / 3：
The M. Riesz-Thorin Interpolation Theorem / 3.1：
Generalized Young's Inequality / 3.2.0.1：
The Hausdorff-Young Inequality / 3.2.0.2：
Stein's Complex Interpolation Theorem / 3.2.1：
The Conjugate Function or Discrete Hilbert Transform / 3.3：
L[superscript p] Theory of the Conjugate Function / 3.3.1：
L[superscript 1] Theory of the Conjugate Function / 3.3.2：
Identification as a Singular Integral / 3.3.2.1：
The Hilbert Transform on R / 3.4：
L[superscript 2] Theory of the Hilbert Transform / 3.4.1：
L[superscript p] Theory of the Hilbert Transform, 1 [ p [ [infinity] / 3.4.2：
Applications to Convergence of Fourier Integrals / 3.4.2.1：
L[superscript 1] Theory of the Hilbert Transform and Extensions / 3.4.3：
Kolmogorov's Inequality for the Hilbert Transform / 3.4.3.1：
Application to Singular Integrals with Odd Kernels / 3.4.4：
Hardy-Littlewood Maximal Function / 3.5：
Application to the Lebesgue Differentiation Theorem / 3.5.1：
Application to Radial Convolution Operators / 3.5.2：
Maximal Inequalities for Spherical Averages / 3.5.3：
The Marcinkiewicz Interpolation Theorem / 3.6：
Calderon-Zygmund Decomposition / 3.7：
A Class of Singular Integrals / 3.8：
Properties of Harmonic Functions / 3.9：
General Properties / 3.9.1：
Representation Theorems in the Disk / 3.9.2：
Representation Theorems in the Upper Half-Plane / 3.9.3：
Herglotz/Bochner Theorems and Positive Definite Functions / 3.9.4：
Poisson Summation Formula And Multiple Fourier Series / 4：
The Poisson Summation Formula in R[superscript 1] / 4.1：
Periodization of a Function / 4.2.1：
Statement and Proof / 4.2.2：
Shannon Sampling / 4.2.3：
Multiple Fourier Series / 4.3：
Basic L[superscript 1] Theory / 4.3.1：
Pointwise Convergence for Smooth Functions / 4.3.1.1：
Representation of Spherical Partial Sums / 4.3.1.2：
Basic L[superscript 2] Theory / 4.3.2：
Restriction Theorems for Fourier Coefficients / 4.3.3：
Poisson Summation Formula in R[superscript d] / 4.4：
Simultaneous Nonlocalization / 4.4.1：
Application to Lattice Points / 4.5：
Kendall's Mean Square Error / 4.5.1：
Landau's Asymptotic Formula / 4.5.2：
Application to Multiple Fourier Series / 4.5.3：
Three-Dimensional Case / 4.5.3.1：
Higher-Dimensional Case / 4.5.3.2：
Schrodinger Equation and Gauss Sums / 4.6：
Distributions on the Circle / 4.6.1：
The Schrodinger Equation on the Circle / 4.6.2：
Recurrence of Random Walk / 4.7：
Applications to Probability Theory / 5：
Basic Definitions / 5.1：
The Central Limit Theorem / 5.2.1：
Restatement in Terms of Independent Random Variables / 5.2.1.1：
Extension to Gap Series / 5.3：
Extension to Abel Sums / 5.3.1：
Weak Convergence of Measures / 5.4：
An Improved Continuity Theorem / 5.4.1：
Another Proof of Bochner's Theorem / 5.4.1.1：
Convolution Semigroups / 5.5：
The Berry-Esseen Theorem / 5.6：
Extension to Different Distributions / 5.6.1：
The Law of the Iterated Logarithm / 5.7：
Introduction to Wavelets / 6：
Heuristic Treatment of the Wavelet Transform / 6.1：
Wavelet Transform / 6.2：
Wavelet Characterization of Smoothness / 6.2.0.1：
Haar Wavelet Expansion / 6.3：
Haar Functions and Haar Series / 6.3.1：
Haar Sums and Dyadic Projections / 6.3.2：
Completeness of the Haar Functions / 6.3.3：
Haar Series in C[subscript 0] and L[subscript p] Spaces / 6.3.3.1：
Pointwise Convergence of Haar Series / 6.3.3.2：
Construction of Standard Brownian Motion / 6.3.4：
Haar Function Representation of Brownian Motion / 6.3.5：
Proof of Continuity / 6.3.6：
Levy's Modulus of Continuity / 6.3.7：
Multiresolution Analysis / 6.4：
Orthonormal Systems and Riesz Systems / 6.4.1：
Scaling Equations and Structure Constants / 6.4.2：
From Scaling Function to MRA / 6.4.3：
Additional Remarks / 6.4.3.1：
Meyer Wavelets / 6.4.4：
From Scaling Function to Orthonormal Wavelet / 6.4.5：
Direct Proof that V[subscript 1] [minus sign in circle] V[subscript 0] Is Spanned by {[Psi](t - k)}[subscript k[set membership]Z] / 6.4.5.1：
Null Integrability of Wavelets Without Scaling Functions / 6.4.5.2：
Wavelets with Compact Support / 6.5：
From Scaling Filter to Scaling Function / 6.5.1：
Explicit Construction of Compact Wavelets / 6.5.2：
Daubechies Recipe / 6.5.2.1：
Hernandez-Weiss Recipe / 6.5.2.2：
Smoothness of Wavelets / 6.5.3：
A Negative Result / 6.5.3.1：
Cohen's Extension of Theorem 6.5.1 / 6.5.4：
Convergence Properties of Wavelet Expansions / 6.6：
Wavelet Series in L[superscript p] Spaces / 6.6.1：
Large Scale Analysis / 6.6.1.1：
Almost-Everywhere Convergence / 6.6.1.2：
Convergence at a Preassigned Point / 6.6.1.3：
Jackson and Bernstein Approximation Theorems / 6.6.2：
Wavelets in Several Variables / 6.7：
Two Important Examples / 6.7.1：
Tensor Product of Wavelets / 6.7.1.1：
General Formulation of MRA and Wavelets in R[superscript d] / 6.7.2：
Notations for Subgroups and Cosets / 6.7.2.1：
Riesz Systems and Orthonormal Systems in R[superscript d] / 6.7.2.2：
Scaling Equation and Structure Constants / 6.7.2.3：
Existence of the Wavelet Set / 6.7.2.4：
Proof That the Wavelet Set Spans V[subscript 1] [minus sign in circle] V[subscript 0] / 6.7.2.5：
Cohen's Theorem in R[superscript d] / 6.7.2.6：
Examples of Wavelets in R[superscript d] / 6.7.3：
References
Notations
Index
Fourier Series on the Circle / 1：
Motivation and Heuristics / 1.1：
Motivation from Physics / 1.1.1：
24.

図書
図書
24. Wavelets and signal processing
Lokenath Debnath, editor
出版情報: Boston : Birkhäuser, c2003  xxv, 435 p. ; 25 cm
シリーズ名: Applied and numerical harmonic analysis / series editor, John J. Benedetto
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25.

図書
図書
25. Wavelets and multiwavelets
Fritz Keinert
出版情報: Boca Raton : Chapman & Hall/CRC, c2004  xii, 275 p. ; 25 cm
シリーズ名: Studies in advanced mathematics
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26.

図書
図書
26. Nonlinear hyperbolic equations, spectral theory, and wavelet transformations : a volume of advances in partial differential equations (:us ; :sz)
Sergio Albeverio ... [et al], editors
出版情報: Basel : Birkhäuser, c2003  [vii], 437 p. ; 24 cm
シリーズ名: Operator theory : advances and applications ; v. 145
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27.

図書
図書
27. Wavelet transforms and time-frequency signal analysis
Lokenath Debnath, editor
出版情報: Boston : Birkhäuser, c2001  xx, 423 p., [8] p. of plates ; 25 cm
シリーズ名: Applied and numerical harmonic analysis / series editor, John J. Benedetto
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目次情報: 続きを見る
Preface Contributors Color Insert
Wavelets and Wavelet / I：
Transforms Wavelet Frames: Multiresolution Analysis and Extension Principles / J.J. Benedetto ; O.M. Treiber
Convergence Rates of Multiscale and Wavelet Expansions / M.A. Kon ; L.A. Raphael Denoising via
Nonorthogonal Wavelet Transforms / K. Berkner ; R.O. Wells ; Jr. Osiris
Wavelets and the Dipole Gas / G. Battle
Wavelets in Closed Forms / A. Zayed ; G.G. Walter
Wavelet Galerkin Methods for Boundary Integral Equations and the Coupling with Finite Element Methods / C. PFrez ; R. Schneider
Computing and Analyzing Turbulent Flows Using Wavelets / K. Schneider ; M. Farge
The Uncertainty Principle for the Short-Time Fourier Transform and Wavelet Transform / L. Cohen
Time-Frequency Signal Analysis Quadratic Time-Frequency Analysis of Linear, Time-Varying Systems / F. Hlawatsch ; G. MatzII：
Inequalities in Mellin--Fourier Signal Analysis / P. Flandrin
Introduction to Time-Frequency Signal Analysis / B. Boashash ; B. Barkat
Reduced Interference Time-Frequency Distributions: Scaled Decompositions and Interpretations / W.J. Williams
Index
Preface Contributors Color Insert
Wavelets and Wavelet / I：
Transforms Wavelet Frames: Multiresolution Analysis and Extension Principles / J.J. Benedetto ; O.M. Treiber
28.

図書
図書
28. Wavelets : algorithms & applications
Yves Meyer ; translated and revised by Robert D. Ryan
出版情報: Philadelphia : Society for Industrial and Applied Mathematics, 1993  xi, 133 p. ; 25 cm
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29.

図書
図書
29. Wavelets and subbands : fundamentals and applications
Agostino Abbate, Casimer M. DeCusatis, Pankaj K. Das
出版情報: Boston : Birkhäuser, c2002  xvii, 551 p. ; 25 cm
シリーズ名: Applied and numerical harmonic analysis / series editor, John J. Benedetto
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目次情報: 続きを見る
Preface
Notation
Introduction / 1.：
Historical Review: From Fourier Analysis to Wavelet Analysis and Subband / 1.1：
Organization of This Book / 1.2：
References / 1.3：
Fundamentals / Part I：
Wavelet Fundamentals / 2.：
Why Wavelet Transforms? / 2.1：
Fourier Transform as a Wave Transform / 2.3：
Wavelet Transform / 2.4：
Connection Between Wavelets and Filters / 2.5：
Time-Frequency Analysis: Short-Time Fourier Transform, Gabor Transform, and Tiling in the Time-Frequency Plane / 2.6：
Examples of Wavelets / 2.7：
From the Continuous to the Discrete Case / 2.8：
Frames / 2.9：
Subbands / 2.10：
Multiresolution Analysis / 2.11：
Matrix Formulation / 2.12：
Multiresolution Revisited / 2.13：
Two-Dimensional Case / 2.14：
DWT and Subband Example / 2.15：
Implementations / 2.16：
Summary and Conclusions / 2.17：
Wavelets and Subbands / 2.18：
Time and Frequency Analysis of Signals / 3.：
Fundamentals of Signal Analysis / 3.1：
Uncertainty Principle / 3.1.2：
Windowed Fourier Transform: Short-Time Fourier Transform and Gabor Transform / 3.2：
General Properties of the Windowed Fourier Transform / 3.2.1：
Uncertainty Principle for Windowed Fourier Transform / 3.2.2：
Inverse Windowed Fourier Transform / 3.2.3：
Continuous Wavelet Transform / 3.3：
Mathematics of the Continuous Wavelet Transform / 3.3.1：
Properties of the Continuous Wavelet Transform / 3.3.2：
Inverse Wavelet Transform / 3.3.3：
Examples of Mother Wavelets / 3.3.4：
Analytic Wavelet Transform / 3.4：
Analytic Signals / 3.4.1：
Analytic Wavelet Transform on Real Signals / 3.4.2：
Physical Interpretation of an Analytic Signal / 3.4.3：
Quadratic Time-Frequency Distributions / 3.5：
Discrete Wavelet Transform: From Frames to Fast Wavelet Transform / 3.6：
Fundamentals of Frame Theory / 4.1：
Sampling Theorem / 4.3：
Wavelet Frames / 4.4：
Examples of Wavelet Frames / 4.5：
Time-Frequency Localization / 4.6：
Orthonormal Discrete Wavelet Transforms / 4.7：
Scaling Functions / 4.8：
Construction of Wavelet Bases Using Multiresolution Analysis / 4.10：
Wavelet Bases / 4.11：
Shannon Wavelet / 4.11.1：
Meyer Wavelet / 4.11.2：
Haar Wavelet / 4.11.3：
Battle-Lemarie (Spline) Wavelets / 4.11.4：
Daubechies Compactly Supported Wavelets / 4.12：
Fast Wavelet Transform / 4.13：
Biorthogonal Wavelet Bases / 4.14：
Theory of Subband Decomposition / 4.15：
Fundamentals of Digital Signal Processing / 5.1：
Multirate Systems / 5.3：
Polyphase Decomposition / 5.4：
Two-Channel Filter Bank/PR Filter / 5.5：
Biorthogonal Filters / 5.6：
Lifting Scheme / 5.7：
M-Band Case / 5.8：
Applications of Multirate Filtering / 5.9：
Two-Dimensional Wavelet Transforms and Applications / 5.10：
Orthogonal Pyramid Transforms / 6.1：
Progressive Transforms for Lossless and Lossy Image Coding / 6.3：
Embedded Zerotree Wavelets / 6.4：
Applications / 6.5：
Applications of Wavelets in the Analysis of Transient Signals / 7.：
Introduction to Time-Frequency Analysis of Transient Signals / 7.1：
Ultrasonic Systems / 7.2.1：
Ultrasonic Characterization of Coatings by the Ridges of the Analytic Wavelet Transform / 7.2.2：
Characterization of Coatings / 7.2.3：
Biomedical Application of Wavelets: Analysis of EEG Signals for Monitoring Depth of Anesthesia / 7.3：
Wavelet Spectral Analysis of EEG Signals / 7.3.1：
System Response Wavelet Analysis of EEG Signals / 7.3.2：
Discussion of Results / 7.3.3：
Applications of Subband and Wavelet Transform in Communication Systems / 7.4：
Applications in Spread Spectrum Communication Systems / 8.1：
Excision / 8.2.1：
Adaptive Filter-Bank Exciser / 8.2.2：
Transform-Based Low Probability of Intercept Receiver / 8.2.3：
Application of Multirate Filter Bank in Spreading Code Generation and Multiple Access / 8.2.4：
Modulation Using Filter Banks and Wavelets / 8.3：
Multitione Modulation / 8.4：
Noise Reduction in Audio and Images Using Wavelets / 8.5：
Audio/Video/Image Compression / 8.6：
Progressive Pattern Recognition
Real-Time Implementations of Wavelet Transforms / 8.7：
Digital VLSI Implementation / 9.1：
Optical Implementation / 9.2：
Matrix Processing and Neural Networks / 9.2.1：
Acousto-Optic Devices / 9.2.2：
Other Optical Implementations / 9.2.3：
Appendix / 9.3：
Fourier Transform / A.：
Discrete Fourier Transform / B.：
z-Transform / C.：
Orthogonal Representation of Signals / D.：
Bibliography
Index
Preface
Notation
Introduction / 1.：
30.

図書
図書
30. Wavelets in numerical simulation : problem adapted construction and applications
Karsten Urban
出版情報: Berlin : Springer, c2002  xv, 181 p. ; 24 cm
シリーズ名: Lecture notes in computational science and engineering ; 22
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31.

図書
図書
31. Wavelet transforms and localization operators
M.W. Wong
出版情報: Basel : Birkhäuser, c2002  vi, 156 p. ; 24 cm
シリーズ名: Operator theory : advances and applications ; v. 136
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32.

図書
図書
32. A first course in wavelets with Fourier analysis
Albert Boggess, Francis J. Narcowich
出版情報: Upper Saddle River, NJ : Prentice Hall, c2001  xix, 283 p. ; 25 cm
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目次情報: 続きを見る
Preface
Acknowledgments
Inner Product Spaces / 0：
Motivation / 0.1：
Definition of Inner Product / 0.2：
The Spaces L[superscript 2] and l[superscript 2] / 0.3：
Definitions / 0.3.1：
Convergence in L[superscript 2] versus Uniform Convergence / 0.3.2：
Schwarz and Triangle Inequalities / 0.4：
Orthogonality / 0.5：
Definitions and Examples / 0.5.1：
Orthogonal Projections / 0.5.2：
Gram-Schmidt Orthogonalization / 0.5.3：
Linear Operators and Their Adjoints / 0.6：
Linear Operators / 0.6.1：
Adjoints / 0.6.2：
Least Squares and Linear Predictive Coding / 0.7：
Best Fit Line for Data / 0.7.1：
General Least Squares Algorithm / 0.7.2：
Linear Predictive Coding / 0.7.3：
Exercises / 0.8：
Fourier Series / 1：
Introduction / 1.1：
Historical Perspective / 1.1.1：
Signal Analysis / 1.1.2：
Partial Differential Equations / 1.1.3：
Computation of Fourier Series / 1.2：
On the Interval -[pi] [less than or equal] x [less than or equal] [pi] / 1.2.1：
Other Intervals / 1.2.2：
Cosine and Sine Expansions / 1.2.3：
Examples / 1.2.4：
The Complex Form of Fourier Series / 1.2.5：
Convergence Theorems for Fourier Series / 1.3：
The Riemann-Lebesgue Lemma / 1.3.1：
Convergence at a Point of Continuity / 1.3.2：
Convergence at a Point of Discontinuity / 1.3.3：
Uniform Convergence / 1.3.4：
Convergence in the Mean / 1.3.5：
The Fourier Transform / 1.4：
Informal Development of the Fourier Transform / 2.1：
The Fourier Inversion Theorem / 2.1.1：
Properties of the Fourier Transform / 2.1.2：
Basic Properties / 2.2.1：
Fourier Transform of a Convolution / 2.2.2：
Adjoint of the Fourier Transform / 2.2.3：
Plancherel Formula / 2.2.4：
Linear Filters / 2.3：
Time Invariant Filters / 2.3.1：
Causality and the Design of Filters / 2.3.2：
The Sampling Theorem / 2.4：
The Uncertainty Principle / 2.5：
Discrete Fourier Analysis / 2.6：
The Discrete Fourier Transform / 3.1：
Definition of Discrete Fourier Transform / 3.1.1：
Properties of the Discrete Fourier Transform / 3.1.2：
The Fast Fourier Transform / 3.1.3：
The FFT Approximation to the Fourier Transform / 3.1.4：
Application--Parameter Identification / 3.1.5：
Application--Discretizations of Ordinary Differential Equations / 3.1.6：
Discrete Signals / 3.2：
Time Invariant, Discrete Linear Filters / 3.2.1：
Z-Transform and Transfer Functions / 3.2.2：
Haar Wavelet Analysis / 3.3：
Why Wavelets? / 4.1：
Haar Wavelets / 4.2：
The Haar Scaling Function / 4.2.1：
Basic Properties of the Haar Scaling Function / 4.2.2：
The Haar Wavelet / 4.2.3：
Haar Decomposition and Reconstruction Algorithms / 4.3：
Decomposition / 4.3.1：
Reconstruction / 4.3.2：
Filters and Diagrams / 4.3.3：
Summary / 4.4：
Multiresolution Analysis / 4.5：
The Multiresolution Framework / 5.1：
Definition / 5.1.1：
The Scaling Relation / 5.1.2：
The Associated Wavelet and Wavelet Spaces / 5.1.3：
Decomposition and Reconstruction Formulas: A Tale of Two Bases / 5.1.4：
Implementing Decomposition and Reconstruction / 5.1.5：
The Decomposition Algorithm / 5.2.1：
The Reconstruction Algorithm / 5.2.2：
Processing a Signal / 5.2.3：
Fourier Transform Criteria / 5.3：
The Scaling Function / 5.3.1：
Orthogonality via the Fourier Transform / 5.3.2：
The Scaling Equation via the Fourier Transform / 5.3.3：
Iterative Procedure for Constructing the Scaling Function / 5.3.4：
The Daubechies Wavelets / 5.4：
Daubechies's Construction / 6.1：
Classification, Moments, and Smoothness / 6.2：
Computational Issues / 6.3：
The Scaling Function at Dyadic Points / 6.4：
Other Wavelet Topics / 6.5：
Computational Complexity / 7.1：
Wavelet Algorithm / 7.1.1：
Wavelet Packets / 7.1.2：
Wavelets in Higher Dimensions / 7.2：
Relating Decomposition and Reconstruction / 7.3：
Transfer Function Interpretation / 7.3.1：
Wavelet Transform / 7.4：
Definition of the Wavelet Transform / 7.4.1：
Inversion Formula for the Wavelet Transform / 7.4.2：
Technical Matters / Appendix A：
Proof of the Fourier Inversion Formula / A.1：
Rigorous Proof of Theorem 5.17 / A.2：
Proof of Theorem 5.10 / A.2.1：
Proof of the Convergence Part of Theorem 5.23 / A.2.2：
Matlab Routines / Appendix B：
General Compression Routine / B.1：
Use of MATLAB's FFT Routine for Filtering and Compression / B.2：
Sample Routines Using MATLAB's Wavelet Toolbox / B.3：
MATLAB Code for the Algorithms in Section 5.2 / B.4：
Bibliography
Index
Preface
Acknowledgments
Inner Product Spaces / 0：
33.

図書
図書
33. An introduction to wavelet analysis
David F. Walnut
出版情報: Boston : Birkhäuser, c2002  xvii, 449 p. ; 25 cm
シリーズ名: Applied and numerical harmonic analysis / series editor, John J. Benedetto
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目次情報: 続きを見る
Preface
Preliminaries / Part I：
Functions and Convergence
Fourier Series
The Fourier Transform
Signals and Systems
The Haar System / Part II：
The Discrete Haar Transform
Orthonormal Wavelet Bases / Part III：
Mulitresolution Analysis
The Discrete Wavelet Transform
Smooth, Compactly Supported Wavelets
Other Wavelet Constructions / Part IV：
Biorthogonal Wavelets
Wavelet Packets
Applications / Part V：
Image Compression
Integral Operators
Review of Advanced Calculus and Linear Algebra / Appendix A：
Excursions in Wavelet Theory / Appendix B：
References Cited in the Text / Appendix C：
Index
Preface
Preliminaries / Part I：
Functions and Convergence
34.

図書
図書
34. Wavelets and other orthogonal systems. 2nd ed
Gilbert G. Walter, Xiaoping Shen
出版情報: Boca Raton, Fla. : Chapman & Hall/CRC, c2001  xx, 370 p. ; 24 cm
シリーズ名: Studies in advanced mathematics
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目次情報: 続きを見る
Preface to first edition
Preface to second edition
List of Figures
Orthogonal Series / 1：
General theory / 1.1：
Examples / 1.2：
Trigonometric system / 1.2.1：
Haar system / 1.2.2：
The Shannon system / 1.2.3：
Problems / 1.3：
A Primer on Tempered Distributions / 2：
Intuitive introduction / 2.1：
Test functions / 2.2：
Tempered distributions / 2.3：
Simple properties based on duality / 2.3.1：
Further properties / 2.3.2：
Fourier transforms / 2.4：
Periodic distributions / 2.5：
Analytic representations / 2.6：
Sobolev spaces / 2.7：
An Introduction to Orthogonal Wavelet Theory / 2.8：
Multiresolution analysis / 3.1：
Mother wavelet / 3.2：
Reproducing kernels and a moment condition / 3.3：
Regularity of wavelets as a moment condition / 3.4：
More on example 3 / 3.4.1：
Mallat's decomposition and reconstruction algorithm / 3.5：
Filters / 3.6：
Convergence and Summability of Fourier Series / 3.7：
Pointwise convergence / 4.1：
Summability / 4.2：
Gibbs phenomenon / 4.3：
Wavelets and Tempered Distributions / 4.4：
Multiresolution analysis of tempered distributions / 5.1：
Wavelets based on distributions / 5.2：
Distribution solutions of dilation equations / 5.2.1：
A partial distributional multiresolution analysis / 5.2.2：
Distributions with point support / 5.3：
Approximation with impulse trains / 5.4：
Orthogonal Polynomials / 5.5：
Classical orthogonal polynomials / 6.1：
Legendre polynomials / 6.2.1：
Jacobi polynomials / 6.2.2：
Laguerre polynomials / 6.2.3：
Hermite polynomials / 6.2.4：
Other Orthogonal Systems / 6.3：
Self adjoint eigenvalue problems on finite intervals / 7.1：
Hilbert-Schmidt integral operators / 7.2：
An anomaly: the prolate spheroidal functions / 7.3：
A lucky accident? / 7.4：
Rademacher functions / 7.5：
Walsh function / 7.6：
Periodic wavelets / 7.7：
Periodizing wavelets / 7.7.1：
Periodic wavelets from scratch / 7.7.2：
Local sine or cosine basis / 7.8：
Biorthogonal wavelets / 7.9：
Pointwise Convergence of Wavelet Expansions / 7.10：
Reproducing kernel delta sequences / 8.1：
Positive and quasi-positive delta sequences / 8.2：
Local convergence of distribution expansions / 8.3：
Convergence almost everywhere / 8.4：
Rate of convergence of the delta sequence / 8.5：
Other partial sums of the wavelet expansion / 8.6：
Positive scaling functions / 8.7：
A general construction / 8.8.1：
Back to wavelets / 8.8.2：
A Shannon Sampling Theorem in Wavelet Subspaces / 8.9：
A Riesz basis of V[subscript m] / 9.1：
The sampling sequence in V[subscript m] / 9.2：
Examples of sampling theorems / 9.3：
The sampling sequence in T[subscript m] / 9.4：
Shifted sampling / 9.5：
Gibbs phenomenon for sampling series / 9.6：
The Shannon case revisited / 9.6.1：
Irregular sampling in wavelet subspaces / 9.6.2：
Extensions of Wavelet Sampling Theorems / 9.8：
Oversampling with scaling functions / 10.1：
Hybrid sampling series / 10.2：
Positive hybrid sampling / 10.3：
The convergence of the positive hybrid series / 10.4：
Cardinal scaling functions / 10.5：
Interpolating multiwavelets / 10.6：
Orthogonal finite element multiwavelets / 10.7：
Sobolev type norm / 10.7.1：
The mother multiwavelets / 10.7.2：
Translation and Dilation Invariance in Orthogonal Systems / 10.8：
Orthogonal polynomials / 11.1：
An example where everything works / 11.3：
An example where nothing works / 11.4：
Weak translation invariance / 11.5：
Dilations and other operations / 11.6：
Analytic Representations Via Orthogonal Series / 11.7：
Trigonometric series / 12.1：
Hermite series / 12.2：
Legendre polynomial series / 12.3：
Analytic and harmonic wavelets / 12.4：
Analytic solutions to dilation equations / 12.5：
Analytic representation of distributions by wavelets / 12.6：
Wavelets analytic in the entire complex plane / 12.7：
Orthogonal Series in Statistics / 12.8：
Fourier series density estimators / 13.1：
Hermite series density estimators / 13.2：
The histogram as a wavelet estimator / 13.3：
Smooth wavelet estimators of density / 13.4：
Local convergence / 13.5：
Positive density estimators based on characteristic functions / 13.6：
Positive estimators based on positive wavelets / 13.7：
Numerical experiment / 13.7.1：
Density estimation with noisy data / 13.8：
Other estimation with wavelets / 13.9：
Spectral density estimation / 13.9.1：
Regression estimators / 13.9.2：
Threshold Methods / 13.10：
Orthogonal Systems and Stochastic Processes / 13.11：
K-L expansions / 14.1：
Stationary processes and wavelets / 14.2：
A series with uncorrelated coefficients / 14.3：
Wavelets based on band limited processes / 14.4：
Nonstationary processes / 14.5：
Bibliography / 14.6：
Index
Preface to first edition
Preface to second edition
List of Figures
35.

図書
図書
35. Abstract harmonic analysis of continuous wavelet transforms
Hartmut Führ
出版情報: Berlin : Springer, c2005  x, 193 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1863
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目次情報: 続きを見る
Introduction / 1：
The Point of Departure / 1.1：
Overview of the Book / 1.2：
Preliminaries / 1.3：
Wavelet Transforms and Group Representations / 2：
Haar Measure and the Regular Representation / 2.1：
Coherent States and Resolutions of the Identity / 2.2：
Continuous Wavelet Transforms and the Regular Representation / 2.3：
Discrete Series Representations / 2.4：
Selfadjoint Convolution Idempotents and Support Properties / 2.5：
Discretized Transforms and Sampling / 2.6：
The Toy Example / 2.7：
The Plancherel Transform for Locally Compact Groups / 3：
A Direct Integral View of the Toy Example / 3.1：
Regularity Properties of Borel Spaces / 3.2：
Direct Integrals / 3.3：
Direct Integrals of Hilbert Spaces / 3.3.1：
Direct Integrals of von Neumann Algebras / 3.3.2：
Direct Integral Decomposition / 3.4：
The Dual and Quasi-Dual of a Locally Compact Group / 3.4.1：
Central Decompositions / 3.4.2：
Type I Representations and Their Decompositions / 3.4.3：
Measure Decompositions and Direct Integrals / 3.4.4：
The Plancherel Transform for Unimodular Groups / 3.5：
The Mackey Machine / 3.6：
Operator-Valued Integral Kernels / 3.7：
The Plancherel Formula for Nonunimodular Groups / 3.8：
The Plancherel Theorem / 3.8.1：
Construction Details / 3.8.2：
Plancherel Inversion and Wavelet Transforms / 4：
Fourier Inversion and the Fourier Algebra / 4.1：
Plancherel Inversion / 4.2：
Admissibility Criteria / 4.3：
Admissibility Criteria and the Type I Condition / 4.4：
Wigner Functions Associated to Nilpotent Lie Groups / 4.5：
Admissible Vectors for Group Extensions / 5：
Quasiregular Representations and the Dual Orbit Space / 5.1：
Concrete Admissibility Conditions / 5.2：
Concrete and Abstract Admissibility Conditions / 5.3：
Wavelets on Homogeneous Groups / 5.4：
Zak Transform Conditions for Weyl-Heisenberg Frames / 5.5：
Sampling Theorems for the Heisenberg Group / 6：
The Heisenberg Group and Its Lattices / 6.1：
Main Results / 6.2：
Reduction to Weyl-Heisenberg Systems / 6.3：
Weyl-Heisenberg Frames / 6.4：
Proofs of the Main Results / 6.5：
A Concrete Example / 6.6：
References
Index
Introduction / 1：
The Point of Departure / 1.1：
Overview of the Book / 1.2：
36.

図書
図書
36. Hyperbolic equations and frequency interactions
Luis Caffarelli, Weinan E., editors
出版情報: Providence, R.I. : American Mathematical Society, c1999  xii, 466 p. ; 26 cm
シリーズ名: IAS/Park City mathematics series / [Dan Freed, series editor] ; v. 5
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目次情報: 続きを見る
Nonlinear Schrodinger equations: Introduction / J. Bourgain
Generalities and initial value problems
The initial value problem (continued)
A digressioin: The initial value problem for the KdV equation
1D invariant Gibbs measures
Invariant measures (2D)
Quasi-periodic solutions of Hamiltonian PDE
Time periodic solutions
Time quasi-periodic solutions
Normal forms
Applications of symplectic capacities to Hamiltonian PDE
Remarks on longtime behaviour of the flow of Hamiltonian PDE
Harmonic analysis, wavelets and applications: Introduction / I. C. Daubechies ; A. C. Gilbert
Constructing orthonormal wavelet bases: Multiresolution analysis
Wavelet bases: Construction and algorithms
More wavelet bases
Wavelets in other functional spaces
Pointwise convergence for wavelet expansions
Two-dimensional wavelets and operators
Wavelets and differential equations
References
Lectures on stability and instability of an ideal fluid: Introduction / S. Friedlander
Equations of motion
Initial-boundary value problem
The type of the Euler equations
Vorticity
Steady flows
Stability/instability of an equilibrium state
Two-dimensional spectral problem
"Arnold" criterion for nonlinear stability
Plane parallel shear flow
Instability in a vorticity norm
Sufficient condition for instability
Exponential stretching
Integrable flows
Baroclinic instability
Nonlinear instability
Waves and transport: Introduction / G. Papanicolaou ; L. Ryzhik
The Schrodinger equation
Symmetric hyperbolic systems
Waves in random media
The diffusion approximation
The geophysical applications
Lectures on geometric optics: Introduction / J. Rauch ; M. Keel
Basic linear existence theorems
Examples of propagation of singularities and of energy
Elliptic geometric optics
Linear hyperbolic geometric optics
Basic nonlinear existence theorems
One phase nonlinear geometric optics
Justification of one phase nonlinear geometric optics
Nonlinear Schrodinger equations: Introduction / J. Bourgain
Generalities and initial value problems
The initial value problem (continued)
37.

図書
図書
37. Wavelet analysis : the scalable structure of information
Howard L. Resnikoff, Raymond O. Wells, Jr
出版情報: New York : Springer, c1998  xvi, 435 p. ; 24 cm
所蔵情報: loading…
38.

図書
図書
38. Wavelets and their applications
edited by Mary Beth Ruskai ... [et al.]
出版情報: Boston : Jones and Bartlett, c1992  xiii, 474 p., [4] p. of plates ; 24 cm
シリーズ名: Jones and Bartlett books in mathematics
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