spherical convolution of sF with a radial function psi
There are two S2Funs \(f: \mathbb S^2 /_{s_1} \to \mathbb{C}\) \(g: \mathbb S^2 /_{s_2} \to \mathbb{C}\) given, where \(s_1\) and \(s_2\) denotes the symmetries. Then the convolution \(f*g: {}_{s_2} \backslash SO(3) /_{s_1} \to \mathbb{C}\) is defined by
\[(f * g)(R) = \frac1{4\pi} \int_{S^2} f(R^{-1}\xi) \cdot g(\xi) \, d\xi\]
with \(vol(S^2) = \int_{S^2} 1 \, d\xi = 4\pi\). Note that \(s_1\) is the right symmetry of \(f*g\) and \(s_2\) is the left symmetry.
Syntax
Input
sF, sF1, sF1 | S2FunHarmonic |
psi | S2Kernel |
A | list of Legendre coeficients |
Output
sF | S2FunHarmonic |
SO3F | SO3Fun |