Wavelets, Spline Interpolation and Lie Groups
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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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