Is there a simplification for the following integral:
$\int_{-\infty}^\infty e^{f*g(x)} dx$
I was hoping that one could take cue from the result following from Fubini's theorem that:
$\int_{-\infty}^\infty f*g(x) dx = \left(\int_{-\infty}^\infty g(\xi) d\xi\right)\left(\int_{-\infty}^\infty f(\eta)d\eta\right)$
and arrive at a rigorous simplification for the aforementioned integral. Any comments, or a proof of a simplification is appreciated. On the other hand, if this is a well-known result, please feel free to point me towards sources. Thanks in advance.