Efficient Computation of Fourier Transforms on Compact Groups
نویسنده
چکیده
This paper generalizes the fast Fourier transform algorithm to the computationof Fourier transformson compact Lie groups. The basic technique uses factorization of group elements and Gel'fand-Tsetlin bases to simplify the computations, and may be extended to treat the computation of Fourier transforms of nitely supported distributions on the group. Similar transforms may be deened on homogeneous spaces; in that case we show how special function properties of spherical functions lead to more eecient algorithms. These results may all be viewed as generalizations of the fast Fourier transform algorithmson the circle, and of recent results about Fourier transformson nite groups.
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