Wavelets, Spline Interpolation and Lie Groups

Abstract

The purpose of this speech is to explain my construction of a so-called wavelet basis on stratified Lie groups [4]. I will first recall the classical notion of a wavelet basis, namely an orthonormal basis ψ∈,j,k (1 ≤ ∈ ≤ 2^d - 1, j ∈ Z, k ∈ Z ^d) of L ²(R^d) generated from a finite number of (regular, oscillating and localized) functions xjje by dyadic dilations and translations= ψ∈, j, k(x)=2^jd/² ψ(2^j,x—k).