Softcover ISBN:  9780821808757 
Product Code:  CRMP/18 
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eBook ISBN:  9781470439323 
Product Code:  CRMP/18.E 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
Softcover ISBN:  9780821808757 
eBook: ISBN:  9781470439323 
Product Code:  CRMP/18.B 
List Price:  $270.00 $202.50 
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Softcover ISBN:  9780821808757 
Product Code:  CRMP/18 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
eBook ISBN:  9781470439323 
Product Code:  CRMP/18.E 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
Softcover ISBN:  9780821808757 
eBook ISBN:  9781470439323 
Product Code:  CRMP/18.B 
List Price:  $270.00 $202.50 
MAA Member Price:  $243.00 $182.25 
AMS Member Price:  $216.00 $162.00 

Book DetailsCRM Proceedings & Lecture NotesVolume: 18; 1999; 397 ppMSC: Primary 65; 41; Secondary 42; 94; 81; 62
This work is based on a series of thematic workshops on the theory of wavelets and the theory of splines. Important applications are included. The volume is divided into four parts: Spline Functions, Theory of Wavelets, Wavelets in Physics, and Splines and Wavelets in Statistics.
Part one presents the broad spectrum of current research in the theory and applications of spline functions. Theory ranges from classical univariate spline approximation to an abstract framework for multivariate spline interpolation. Applications include scattereddata interpolation, differential equations and various techniques in CAGD.
Part two considers two developments in subdivision schemes; one for uniform regularity and the other for irregular situations. The latter includes construction of multidimensional wavelet bases and determination of bases with a given time frequency localization.
In part three, the multifractal formalism is extended to fractal functions involving oscillating singularites. There is a review of a method of quantization of classical systems based on the theory of coherent states. Wavelets are applied in the domains of atomic, molecular and condensedmatter physics.
In part four, ways in which wavelets can be used to solve important function estimation problems in statistics are shown. Different wavelet estimators are proposed in the following distinct cases: functions with discontinuities, errors that are no longer Gaussian, wavelet estimation with robustness, and error distribution that is no longer stationary.
Some of the contributions in this volume are current research results not previously available in monograph form. The volume features many applications and interesting new theoretical developments. Readers will find powerful methods for studying irregularities in mathematics, physics, and statistics.
Titles in this series are copublished with the Centre de Recherches Mathématiques.
ReadershipGraduate students, mathematicians, physicists, and statisticians working in approximation theory, mathematical analysis, image processing, signal analysis, mathematical physics, and function estimation.

Table of Contents

Spline Functions

Introduction and summary

Radial extensions of vertex data

The use of splines in the numerical solutions of differential and Volterra integral equations

On best error bounds for deficient splines

Optimal error bounds for spline interpolation on a uniform partition

Modelization of flexible objects using constrained optimization and Bspline surfaces

New control polygons for polynomial curves

Splines in approximation and differential operators: $(m,\ell ,s)$ interpolatingspline

New families of Bsplines on uniform meshes of the plane

Theory of Wavelets

Introduction and summary

Analysis of Hermiteinterpolatory subdivision schemes

Some directional microlocal classes defined using wavelet transforms

Nonseparable biorthogonal wavelet bases of $L^2(\mathbb R^n)$

Local bases: Theory and applications

On the $L^p$Lipschitz exponents of the scaling functions

Robust speech and speaker recognition using instantaneous frequencies and amplitudes obtained with waveletderived synchrosqueezing measures

Extensions of the Heisenberg group and wavelet analysis in the plane

Wavelets in physics

Introduction and summary

Coherent states and quantization

Wavelets in molecular and condensedmatter physics

Wavelets in atomic physics

The wavelet $\epsilon $expansion and Hausdorff dimension

Modelling the coupling between small and large scales in the KuramotoSivashinsky equation

Continuous wavelet transform analysis of onedimensional quantum ground states

Oscillating singularities and fractal functions

Splines and Wavelets in Statistics

Introduction and summary

Wavelet estimators for changepoint regression models

Wavelet thresholding for non (necessarily) Guassian noise: A preliminary report

DeslauriesDubuc: Ten years after

Some theory for $L$spline smoothing

Spectral representation and estimation for locally stationary wavelet processes


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This work is based on a series of thematic workshops on the theory of wavelets and the theory of splines. Important applications are included. The volume is divided into four parts: Spline Functions, Theory of Wavelets, Wavelets in Physics, and Splines and Wavelets in Statistics.
Part one presents the broad spectrum of current research in the theory and applications of spline functions. Theory ranges from classical univariate spline approximation to an abstract framework for multivariate spline interpolation. Applications include scattereddata interpolation, differential equations and various techniques in CAGD.
Part two considers two developments in subdivision schemes; one for uniform regularity and the other for irregular situations. The latter includes construction of multidimensional wavelet bases and determination of bases with a given time frequency localization.
In part three, the multifractal formalism is extended to fractal functions involving oscillating singularites. There is a review of a method of quantization of classical systems based on the theory of coherent states. Wavelets are applied in the domains of atomic, molecular and condensedmatter physics.
In part four, ways in which wavelets can be used to solve important function estimation problems in statistics are shown. Different wavelet estimators are proposed in the following distinct cases: functions with discontinuities, errors that are no longer Gaussian, wavelet estimation with robustness, and error distribution that is no longer stationary.
Some of the contributions in this volume are current research results not previously available in monograph form. The volume features many applications and interesting new theoretical developments. Readers will find powerful methods for studying irregularities in mathematics, physics, and statistics.
Titles in this series are copublished with the Centre de Recherches Mathématiques.
Graduate students, mathematicians, physicists, and statisticians working in approximation theory, mathematical analysis, image processing, signal analysis, mathematical physics, and function estimation.

Spline Functions

Introduction and summary

Radial extensions of vertex data

The use of splines in the numerical solutions of differential and Volterra integral equations

On best error bounds for deficient splines

Optimal error bounds for spline interpolation on a uniform partition

Modelization of flexible objects using constrained optimization and Bspline surfaces

New control polygons for polynomial curves

Splines in approximation and differential operators: $(m,\ell ,s)$ interpolatingspline

New families of Bsplines on uniform meshes of the plane

Theory of Wavelets

Introduction and summary

Analysis of Hermiteinterpolatory subdivision schemes

Some directional microlocal classes defined using wavelet transforms

Nonseparable biorthogonal wavelet bases of $L^2(\mathbb R^n)$

Local bases: Theory and applications

On the $L^p$Lipschitz exponents of the scaling functions

Robust speech and speaker recognition using instantaneous frequencies and amplitudes obtained with waveletderived synchrosqueezing measures

Extensions of the Heisenberg group and wavelet analysis in the plane

Wavelets in physics

Introduction and summary

Coherent states and quantization

Wavelets in molecular and condensedmatter physics

Wavelets in atomic physics

The wavelet $\epsilon $expansion and Hausdorff dimension

Modelling the coupling between small and large scales in the KuramotoSivashinsky equation

Continuous wavelet transform analysis of onedimensional quantum ground states

Oscillating singularities and fractal functions

Splines and Wavelets in Statistics

Introduction and summary

Wavelet estimators for changepoint regression models

Wavelet thresholding for non (necessarily) Guassian noise: A preliminary report

DeslauriesDubuc: Ten years after

Some theory for $L$spline smoothing

Spectral representation and estimation for locally stationary wavelet processes