How to prove that $f(x)=\sum_{n=-\infty}^\infty f(n)K(x-n)$ where $K(y)=\sin\pi y/\pi y$
Here, $f$ is moderate decrease and its fourier transform is supported in $[-1/2, 1/2]$.
I show that $\hat f(k)=\sum_{n=-\infty}^\infty f(n)e^{-2\pi ink}$ but no improvement...
Plz help