Galilean wavelets: Coherent states of the affine Galilei group

We derive Galilean wavelets, by which we mean coherent states of the affine Galilei group, that is, the Galilei group extended by independent space and time dilations. The construction follows a general method based on square integrable group representations, possibly modulo a subgroup, i.e., on a homogeneous space of the underlying group. We also examine the restriction to the Schrödinger subgroup, which contains only dilations that leave invariant the Schrödinger and the heat equations