N-DIMENSIONAL AFFINE WEYL-HEISENBERG WAVELETS

n-dimensional coherent states systems generated by translations, modul ations, rotations and dilations are described. Starting from unitary i rreducible representations of the n-dimensional affine Weyl-Heisenberg group, which are not square-integrable, one is led to consider system s of coherent states labeled by the elements of quotients of the origi nal group. Such systems can yield a resolution of the identity, and th en be used as alternatives to usual wavelet or windowed Fourier analys is. When the quotient space is the phase space of the representation, different embeddings of it into the group provide different descriptio ns of the phase space.