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I'm looking to change a double integral into convolution from the original integral, which is

$$S(z_0,\Omega) = \int_{4\pi}\frac{H\!\left(z_0,\Omega,\Omega'\right)}{4\pi}\int_{z_0}^{\infty}F\!\left(z',\Omega'\right)G\!\left(z',\Omega'\right)dz'\, d\omega,$$

where $\Omega = [\mu,\phi],\;\mu = \cos(\theta),\;d\omega = \sin\left(\theta'\right)\,d\theta' \,d\phi'$.

Also if it helps, $H$ is an angular distribution function.

I want to find a way to change this into the form of

$$S(z_0,\Omega) = H(z_0,\Omega)\ast_{\Omega'}[F(z,\Omega)\ast_{z'}G(z,\Omega)].$$

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