3
$\begingroup$

let $f\in L^1$ and $g \in L^{\infty}$, 2pi periodic

show $\lim_{n\to \infty} \frac{1}{2\pi} \int_0^{2\pi} f(t) g(nt) dt = \hat{f}(0) \hat{g}(0)$

i tried using expressing the rhs as integrals, but i could not match the lhs

any suggestions?

1 Answers 1