ABSTRACT
Wavelet transform of functions may be understood as a group action on the space of square integrable functions for suitable group. This chapter presents the eventual link between wavelet transforms and the real affine group. It recalls the basic definition of groups. Spherical wavelets are adapted for understanding complicated functions defined or supported by the sphere. The classical are essentially done by convolving the function against rotated and dilated versions of one fixed function. The chapter shows that the scaling functions are suitable candidates to approximate functions in L2 as it is needed in wavelet theory in general and thus they are suitable sources to define multi-resolution analysis and/or a wavelet analysis on the sphere.
