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I have an expression in time space that looks like:

$$z(t-t') = \int_{-\infty}^{\infty} ds \int_{-\infty}^{\infty} ds' f(t-s)g(s-s')h(s'-t')$$

Is this expression considered a triple convolution?* I know the explicit expressions for $f$, $g$ and $h$ in time space $(t-t')$ and their respective Fourier transforms $F$, $G$, $H$ in frequency space ($\nu$).

So if we Fourier transform $z$ from $(t-t')$ to $\nu$, will the result be:

$$Z(\nu) = F(\nu) \cdot G(\nu) \cdot H(\nu)$$

where $\cdot$ is a product?


*In order to prove associativity of convolutions we simply use Fubini's theorem and a triple convolution:

$$ (f \star g) \star h = \iint dv\,du f(u) g(v-u) h(t-v)$$

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