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?
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?