In this paper we describe algorithms for the numerical computation of Fourier transforms of tensor elds on the two-sphere, S. These algorithms reduce the computation of an expansion on tensor spherical harmonics to expansions in scalar spherical harmonics, and hence can take advantage of recent improvements in the eÆciency of computation of scalar spherical harmonic transforms.

Spherical harmonics are employed in a wide range of applications in computational science and physics, and many of them require the rotation of functions. We present an efficient and accurate algorithm for the rotation of finite spherical harmonics expansions. Exploiting the pointwise action of the rotation group on functions on the sphere, we obtain the spherical harmonics expansion of a rotat...

Author(s) of this paper may load this reprint on their own web site provided that this cover page is retained. Republication of this article or its storage in electronic databases or the like is not permitted without prior permission in writing from the IUCr. A numerically efficient method of constructing symmetric real spherical harmonics is presented. Symmetric spherical harmonics are real sp...

An exact fast algorithm is developed for the spin-weighted spherical harmonics transforms of band-limited spin ±2 functions on the sphere. First, we recall the notion of spin functions on the sphere and their decomposition in an orthonormal basis of spin-weighted spherical harmonics. Second, we discuss the a priori O(L4) asymptotic complexity of the spin ±2 spherical harmonics transforms, where...