# multiplication of a function with a Fourier-transformed equals to Fourier-transformed with a function

I already showed b item using the fact that it is $$h\left(0\right)=\int \:f\left(t\right)g\left(0-t\right)dt$$

I struggle a lot of hours trying to find the trick in item C.

• If you know that $\mathcal{G}$ is the Fourier transform of $g$, do you know the inverse Fourier transform of $g$? – TimWescott Jan 12 at 19:48

$$G(f)=\mathscr{F}\{g(t)\}$$
$$g(f)=\mathscr{F}\{G(-t)\}$$
holds. Then just use the result from $$b$$.