Wavelet Transforms Associated to the n-Dimensional Euclidean Group with Dilations: Signal in More Than One Dimension

When one wants to extend to more than one dimension, the whole wavelet machinery developped for the one dimensional ax+b group, while keeping the group language, it is natural to consider the n-dimensional Euclidean group with dilations, to be denoted by IG(n). It is a non-unimodular locally compact group and its most natural unitary representation of in L(ℝn, dn x), is irreducible and square integrable.