On Some Quaternionic Coherent States and Wavelets

Abstract

As a natural extension of the affine groups of the reals and the complexes, leading to one and two-dimensional wavelets, we look at the quaternionic affine group and its representations on both complex and quaternionic Hilbert spaces. We then study the problem of coherent states and wavelets built from these representations.Mathematics Subject Classification (2010). Primary 81R30; Secondary 57S20.