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 SO(3,1) via the Iwasawa decomposition, and X ~ SOo(3,1)/C. The space L^2(S^2,d mo) 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.