  By analogy with the real and complex affine groups, whose unitary irreducible
representations are used to define the one and two-dimensional continuous
wavelet transforms, we study here the quaternionic affine group and construct
its unitary irreducible representations. These representations are constructed
both on a complex and a quaternionic Hilbert space. As in the real and complex
cases, the representations for the quaternionic group also turn out to be
square-integrable. Using these representations we constrct quaternionic
wavelets and continuous wavelet transforms on both the complex and quaternionic
Hilbert spaces.
