  The Perelomov coherent states of SU(1,1) are labeled by elements of the
quotient of SU(1,1) by the compact subgroup. Taking advantage of the fact that
this quotient is isomorphic to the affine group of the real line, we are able
to parameterize the coherent states by elements of that group or equivalently
by points in the half-plane. Such a formulation permits to find new properties
of the SU(1,1) coherent states and to relate them to affine wavelets.
