Multiresolution Analysis and Wavelets on S 2 and S 3

In this paper, we construct a multiresolution analysis and a wavelet basis on two speciic compact manifolds. Using special charts, the problem is reduced to nding appropriate nested spaces on rectangular domains. The claim of C 1-continuity gives rise to certain boundary conditions on the rectangles. To satisfy these conditions, we use a tensor product approach in which one factor is an exponential spline.