Wavelet transforms via generalized quasi-regular representations
Let \(G\) be a locally compact group, \(H\) a closed subgroup of \(G\). The authors define generalized quasi-regular representations of \(G\) on \(L^2 (G/H)\) and the relevant continuous wavelet transforms. It is shown that this method enables one to obtain \(n\)-dimensional continuous wavelet transforms and also continuous wavelet transforms on a group, which is topologically isomorphic to a homogeneous space of the semidirect product of an abelian locally compact group. Continuous wavelet transforms on some other groups discussed in the previous publications can also be included in this scheme.
scientific article; zbMATH DE number 5545827