I have question regarding convolution of functions (say g and h) defined on Sn. In Fourier space this is equivalent to IFT(G.H), where G = FT(g) and H = FT(h).

Fast Fourier transforms (Clausen's FFT) proceeds by recursively breaking down Fourier transformation over Sn into smaller transforms over S_(n-1), S_(n-2)... and computing each S_(k)-transform from the k independent S_(k-1) transforms.

Now the question I have is - How does the convolution of two functions (g & h, each defined on Sn) translate to S_(n-1)? In other words, is their any defining expression involving G' and H' to provide the n-1 independent S_(n-1) transforms to get final the convolution.

G': descendant Fourier transform of G on S_(n-1) H': descendant Fourier transform of H on S_(n-1) FT: Fourier transform IFT: Inverse Fourier transform

I would appreciate if anyone can direct me to some papers/books which talk about these concepts.

DP