How to show that $\int_{-\infty}^{\infty}|\frac{\sin{nx}\sin{x}}{x^2}|dx \to \infty$ as $n \to \infty$?
A proof of the fact that the Fourier transform is not surjective from $\mathcal{L}^1(\mathbb{R})$ to $C_0( \mathbb{R})$