WAVELETS AND WAVELET FRAMES ON THE 2-SPHERE

We review the construction of the continuous wavelet transform (CWT) on the 2-sphere by two methods, the group-theoretical approach and the geometrical method based on conformal invariance. Then we discuss the discretization of the spherical CWT and build associated discrete wavelet frames, first half-continuous ones (only the scale is discretized), then fully discrete ones. To that effect, we generalize the notion of frame, introducing weighted and controlled frames.