Wavelets, Spline Interpolation and Lie Groups
The purpose of this speech is to explain my construction of a so-called wavelet basis on stratified Lie groups . I will first recall the classical notion of a wavelet basis, namely an orthonormal basis ψ∈,j,k (1 ≤ ∈ ≤ 2d - 1, j ∈ Z, k ∈ Z d) of L 2(Rd) generated from a finite number of (regular, oscillating and localized) functions xjje by dyadic dilations and translations= ψ∈, j, k(x)=2jd/2 ψ(2j,x—k).
KeywordsHeisenberg Group Wavelet Basis Riesz Basis Spline Surface Closed Linear Span
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- JAFFARD, S. These, Ecole Poly technique, 1989.Google Scholar
- MEYER, Y. Ondelettes et operateurs. Tome 1. Paris, Hermann, 1990.Google Scholar
- STROMBERG, J. O. A modified Franklin system and higher-order systems in IRn, in Conf. on Harmonic Analysis in honor of A. Zygmund, vol. 2, 1988, 475–494.Google Scholar