  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.
