Solution
= Solution
With the convention in <convolution theorem>, absolute integrability permits Fubini:
$$
\widehat{f*g}(\xi)=\int\!\int f(y)g(x-y)e^{-2\pi ix\cdot\xi}\,dy\,dx
=\widehat f(\xi)\widehat g(\xi).
$$
= Solution
With the convention in <convolution theorem>, absolute integrability permits Fubini:
$$
\widehat{f*g}(\xi)=\int\!\int f(y)g(x-y)e^{-2\pi ix\cdot\xi}\,dy\,dx
=\widehat f(\xi)\widehat g(\xi).
$$