Technical Report Number
This paper considers the problem of computing the harmonic expansion of functions defined on the sphere. We begin by proving convolution theorems that relate the convolution of two functions on the sphere to a "multiplication" in the sprectral domain, as well as the multiplication of two functions on the sphere to a "convolution" in the spectral domain. These convolution theorems are then used to develop a sampling theorem on the sphere.
Dartmouth Digital Commons Citation
Driscoll, James R. and Healy, Dennis M., "Asymptotically Fast Algorithms for Spherical and Related Transforms" (1989). Computer Science Technical Report PCS-TR89-141. https://digitalcommons.dartmouth.edu/cs_tr/43