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Spline Functions and the Theory of Wavelets
About this Title
Serge Dubuc, Université de Montréal, Montréal, QC, Canada and Gilles Deslauriers, Ecole Polytechnic de Montréal, Montréal, QC, Canada, Editors
Publication: CRM Proceedings and Lecture Notes
Publication Year:
1999; Volume 18
ISBNs: 978-0-8218-0875-7 (print); 978-1-4704-3932-3 (online)
DOI: https://doi.org/10.1090/crmp/018
MathSciNet review: MR1676230
MSC: Primary 65-06; Secondary 41-06, 42-06
ReadershipTable of Contents
Front/Back Matter
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