%0 Journal Article
%T Continuous wavelet transforms from semidirect products: Cyclic representations and Plancherel measure
%A Hartmut Fuehr
%A Matthias Mayer
%J Physics
%D 2001
%I arXiv
%X Continuous wavelet transforms arising from the quasiregular representation of a semidirect product of a vector group with a matrix group -- the so-called dilation group -- have been studied by various authors. Recently the attention has shifted from the irreducible case to include more general dilation groups, for instance cyclic (more generally: discrete) or one-parameter groups. These groups do not give rise to irreducible square-integrable representations, yet it is possible (and quite simple) to give admissibility conditions for a large class of them. We put these results in a theoretical context by establishing a connection to the Plancherel theory of the semidirect products, and show how the admissibility conditions relate to abstract admissibility conditions which use Plancherel theory.
%U http://arxiv.org/abs/math-ph/0102002v1