conv edit page

convolution of an SO3Kernel function with a function or a kernel on SO(3)

We convolute an SO3Kernel \(f\) with another SO3Kernel or an SO3Fun \(g\) by the convolution

\[ (f {*}_L g)(R) = \frac1{8\pi^2} \int_{SO(3)} f(q) \cdot g(q^{-1}\,R) \, dq \]

which in this case is similar to the so caled right sided convolution, see SO3FunHarmonic/conv.

The convolution of an SO3Kernel with an S2Kernel or an S2Fun \(h\) is defined by

\[ (f * h)(\xi) = \frac1{8\pi^2} \int_{SO(3)} f(q) \cdot h(q^{-1}\,\xi) \, dq \].


psi = conv(psi1,psi2)
SO3F2 = conv(psi1,SO3F1)
sF2 = conv(psi1,sF1)
phi2 = conv(psi1,phi1)
psi = conv(psi1)


psi1, psi2 SO3Kernel
phi1 S2Kernel
SO3F1 SO3Fun
sF1 S2Fun


psi SO3Kernel
SO3F2 SO3Fun
sF2 S2Fun
phi2 S2Kernel

See also

SO3FunHarmonic.conv SO3FunRBF.conv S2FunHarmonic.conv S2Kernel.conv