I'm trying to work through the results of a classic paper in super-resolution microscopy (C. Sheppard, Optik, 1988). The main result sort of hinges on writing the double integral:
$$ \int dx \int dx^\prime h_{1}{(x^\prime)}t{(x^\prime - x_{s} - \frac{x}{2})}h_{2}{(x^\prime - x)} $$
into a convolution form:
$$ \{ h_{1}{(2x_{s})} \ast h_{2}{(2x_{s})} \} \ast t{(x_{s})} $$
I'm sure it's just a matter of simple u-substitution, but I'm stuck trying to find it.