Wavelets on the 2-sphere and related manifolds

We present a group-theoretical derivation of the continuous wavelet transform (CWT) on the 2-sphere S-2, based on the construction of coherent states associated to square integrable group representations. The parameter space X is the product of SO(3)XR*+, embedded into the Lorentz group SOo(3, 1) via the Iwasawa decomposition, and X similar or equal to SOo(3, 1)/C. The space L-2(S2, d mu) carries a unitary irreducible representation of SOo(3, 1), which is square integrable over X, and thus yields the wavelets on S-2 and the associated CWT.