Let f and g be $2π-periodic$ integrable functions on $\mathbb{R} $ and let $f ∗ g$ denote their convolution on $[−π, π]$. Prove that $\widehat{f∗g(n)} = \hat{f}(n)\hat{g}(n)$.
I'm stuck with how to solve this, I don't really know where to begin.
Any help is much appreciated.