CRM Proceedings & Lecture Notes 1999; 397 pp; softcover Volume: 18 ISBN10: 0821808753 ISBN13: 9780821808757 List Price: US$128 Member Price: US$102.40 Order Code: CRMP/18
 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. 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  H. Brunner  Introduction and summary
 L. P. Bos and D. Holland  Radial extensions of vertex data
 H. Brunner  The use of splines in the numerical solutions of differential and Volterra integral equations
 F. Dubeau and J. Savoie  On best error bounds for deficient splines
 F. Dubeau and J. Savoie  Optimal error bounds for spline interpolation on a uniform partition
 J.P. Dussault and N. Pfister  Modelization of flexible objects using constrained optimization and Bspline surfaces
 J. C. Fiorot and P. Jeannin  New control polygons for polynomial curves
 A. Le Méhauté and A. Bouhamidi  Splines in approximation and differential operators: \((m,\ell,s)\) interpolatingspline
 P. Sablonnière  New families of Bsplines on uniform meshes of the plane
Theory of Wavelets  S. Jaffard  Introduction and summary
 N. Dyn and D. Levin  Analysis of Hermiteinterpolatory subdivision schemes
 M. Holschneider  Some directional microlocal classes defined using wavelet transforms
 A. Karoui and R. Vaillancourt  Nonseparable biorthogonal wavelet bases of \(L^2(\mathbb R^n)\)
 J. Kovačević and R. Bernardini  Local bases: Theory and applications
 K.S. Lau and M.F. Ma  On the \(L^p\)Lipschitz exponents of the scaling functions
 S. Maes  Robust speech and speaker recognition using instantaneous frequencies and amplitudes obtained with waveletderived synchrosqueezing measures
 E. Schulz and K. F. Taylor  Extensions of the Heisenberg group and wavelet analysis in the plane
Wavelets in Physics  A. Arneodo  Introduction and summary
 S. Twareque Ali  Coherent states and quantization
 J.P. Antoine  Wavelets in molecular and condensedmatter physics
 J.P. Antoine, Ph. Antoine, and B. Piraux  Wavelets in atomic physics
 G. Battle  The wavelet \(\epsilon\)expansion and Hausdorff dimension
 J. Elezgaray, G. Berkooz, and P. Holmes  Modelling the coupling between small and large scales in the KuramotoSivashinsky equation
 C. R. Handy and R. Murenzi  Continuous wavelet transform analysis of onedimensional quantum ground states
 A. Arneodo, E. Bacry, S. Jaffard, and J. F. Muzy  Oscillating singularities and fractal functions
Splines and Wavelets in Statistics  B. Macgibbon  Introduction and summary
 A. Antoniadis  Wavelet estimators for changepoint regression models
 R. Averkamp and C. Houdré  Wavelet thresholding for non (necessarily) Guassian noise: A preliminary report
 D. L. Donoho and T. P. Y. Yu  DeslauriesDubuc: Ten years after
 J. O. Ramsay and N. Heckman  Some theory for \(L\)spline smoothing
 R. von Sachs, G. P. Nason, and G. Kroisandt  Spectral representation and estimation for locally stationary wavelet processes
