This question makes me really confused:
Let $f$ and $g$ two functions in $L^2$. Show that: $\int \widehat f\cdot gdx= \int f\cdot\widehat gdx,$ where $\widehat f$ is the Fourier transform for the function $f$.
Notice that I need to prove it in $L^2$. Can anyone please help me?
Thanks,