Wavelets on the 2-sphere and related manifolds

We present a group-theoretical derivation of the continuous wavelet transform (CWT) on the 2-sphere S2, based on the construction of coherent states associated to square integrable group representations. The parameter space X is the product of SO(3) × R∗+, embedded into the Lorentz group SOo(3,1) via the Iwasawa decomposition, and X ∼-SOo(3,1)/C. The space L2(S2,dμ) carries a unitary irreducible representation of SOo(3,1), which is square integrable over X, and thus yields the wavelets on S2 and the associated CWT.