conv edit page

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

sF = conv(sF, psi)
sF = conv(sF, A)
SO3F = conv(sF1, sF2)

Input

sF, sF1, sF1 S2FunHarmonic
psi S2Kernel
A list of Legendre coeficients

Output

sF S2FunHarmonic
SO3F SO3Fun

See also

S2Kernel.conv SO3FunHarmonic.conv SO3Kernel.conv