## Calculating an auto-convolution integral by Fourier transforms

Recently I came across a forum contribution [1] where the author describes how to use the unitarity of the Fourier transform on $L^2(\RR)$ to compute the definite integral $$\label{eq:I} I(t_0) \DEF \int_{-\infty}^{\infty}{\frac{\sin(\tau – t_0)}{(\tau – t_0)}\frac{\sin(\tau + t_0)}{(\tau + t_0)}\,d\tau},$$ where $t_0 \in \RR$ is a constant. In the… Read moreCalculating an auto-convolution integral by Fourier transforms