Addition theorems for spin spherical harmonics: II. Results

Fast Spin ±2 Spherical Harmonics Transforms

An exact fast algorithm is developed for the direct spin-weighted spherical harmonics transforms of bandlimited spin ±2 functions on the sphere. First, we define 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 2L stan...

Spherical harmonics and integration in superspace II

The study of spherical harmonics in superspace, introduced in [J. Phys. A: Math. Theor. 40 (2007) 7193-7212], is further elaborated. A detailed description of spherical harmonics of degree k is given in terms of bosonic and fermionic pieces, which also determines the irreducible pieces under the action of SO(m) × Sp(2n). In the second part of the paper, this decomposition is used to describe al...

Spherical Harmonics

5 Spherical Harmonics 7 5.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 5.2 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 5.2.1 Harmonic expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 5.2.2 Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

Fast spin ±2 spherical harmonics transforms and application in cosmology

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...

3 Generalized Spherical Harmonics