Based on a new definition of dilation a scale discrete version of spherical multiresolution is described, starting from a
scale discrete wavelet transform on the sphere. Depending on the type of application, different families of wavelets are chosen.
In particular, spherical Shannon wavelets are constructed that form an orthogonal multiresolution analysis. Finally fully
discrete wavelet approximation is discussed in the case of band-limited wavelets.
Key words. Spherical multiresolution analysis, Scaling function, Scale discrete wavelets, Rational wavelets, Exponential wavelets,
Orthogonal (Shannon) wavelets, de La Vallée-Poussin wavelets, Exact fully discrete wavelet transform. AMS Classification.
41A58, 42C15, 44A35, 45E99.
June 18, 1996. Date revised: January 14, 1997.