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Asymptotically Fast Algorithms for Spherical and Related Transforms
James R. Driscoll, Dennis M. Healy
Dartmouth PCS-TR89-141


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.


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   James R. Driscoll and Dennis M. Healy, "Asymptotically Fast Algorithms for Spherical and Related Transforms." Dartmouth Computer Science Technical Report PCS-TR89-141, 1989.

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