Wavelets from square-integrable representations

The continuous wavelet decompositions that arise from square-integrable representations of certain Lie groups on L(2)(R(n)) are investigated. The groups are formed as the semidirect product of R(n) with an n-dimensional subgroup H of GL(n)(R). There is a natural ''translation and dilation'' representation of such groups on L(2)(R(n)). The basic formulas of Duflo and Moore, which lead to the resolution of the identity via a square-integrable representation, are given an elementary proof for this special case; Several two-dimensional examples are described. A method for discrete decompositions via frames is given using the representations under study.