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Spline Functions and the Theory of Wavelets
 
Edited by: Serge Dubuc Université de Montréal, Montréal, QC, Canada
Gilles Deslauriers Ecole Polytechnic de Montréal, Montréal, QC, Canada
A co-publication of the AMS and Centre de Recherches Mathématiques
Spline Functions and the Theory of Wavelets
Softcover ISBN:  978-0-8218-0875-7
Product Code:  CRMP/18
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
eBook ISBN:  978-1-4704-3932-3
Product Code:  CRMP/18.E
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
Softcover ISBN:  978-0-8218-0875-7
eBook: ISBN:  978-1-4704-3932-3
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
Spline Functions and the Theory of Wavelets
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Spline Functions and the Theory of Wavelets
Edited by: Serge Dubuc Université de Montréal, Montréal, QC, Canada
Gilles Deslauriers Ecole Polytechnic de Montréal, Montréal, QC, Canada
A co-publication of the AMS and Centre de Recherches Mathématiques
Softcover ISBN:  978-0-8218-0875-7
Product Code:  CRMP/18
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
eBook ISBN:  978-1-4704-3932-3
Product Code:  CRMP/18.E
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
Softcover ISBN:  978-0-8218-0875-7
eBook ISBN:  978-1-4704-3932-3
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 Details
     
     
    CRM Proceedings & Lecture Notes
    Volume: 181999; 397 pp
    MSC: 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 scattered-data 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 condensed-matter 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 co-published with the Centre de Recherches Mathématiques.

    Readership

    Graduate 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 B-spline surfaces
    • New control polygons for polynomial curves
    • Splines in approximation and differential operators: $(m,\ell ,s)$ interpolating-spline
    • New families of B-splines on uniform meshes of the plane
    • Theory of Wavelets
    • Introduction and summary
    • Analysis of Hermite-interpolatory 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 wavelet-derived 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 condensed-matter physics
    • Wavelets in atomic physics
    • The wavelet $\epsilon $-expansion and Hausdorff dimension
    • Modelling the coupling between small and large scales in the Kuramoto-Sivashinsky equation
    • Continuous wavelet transform analysis of one-dimensional quantum ground states
    • Oscillating singularities and fractal functions
    • Splines and Wavelets in Statistics
    • Introduction and summary
    • Wavelet estimators for change-point regression models
    • Wavelet thresholding for non (necessarily) Guassian noise: A preliminary report
    • Deslauries-Dubuc: Ten years after
    • Some theory for $L$-spline smoothing
    • Spectral representation and estimation for locally stationary wavelet processes
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 181999; 397 pp
MSC: 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 scattered-data 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 condensed-matter 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 co-published with the Centre de Recherches Mathématiques.

Readership

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 B-spline surfaces
  • New control polygons for polynomial curves
  • Splines in approximation and differential operators: $(m,\ell ,s)$ interpolating-spline
  • New families of B-splines on uniform meshes of the plane
  • Theory of Wavelets
  • Introduction and summary
  • Analysis of Hermite-interpolatory 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 wavelet-derived 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 condensed-matter physics
  • Wavelets in atomic physics
  • The wavelet $\epsilon $-expansion and Hausdorff dimension
  • Modelling the coupling between small and large scales in the Kuramoto-Sivashinsky equation
  • Continuous wavelet transform analysis of one-dimensional quantum ground states
  • Oscillating singularities and fractal functions
  • Splines and Wavelets in Statistics
  • Introduction and summary
  • Wavelet estimators for change-point regression models
  • Wavelet thresholding for non (necessarily) Guassian noise: A preliminary report
  • Deslauries-Dubuc: Ten years after
  • Some theory for $L$-spline smoothing
  • Spectral representation and estimation for locally stationary wavelet processes
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