We set $\sigma^{\prime} = \frac{1}{2\pi\sigma}$. Show that there exists a real $\mu$ such that $\mathcal{F}\left(g_{\sigma}\right) = \mu g_{\sigma^{\prime}}$. The value of $\mu$ need not be made explicit.
We set $\sigma^{\prime} = \frac{1}{2\pi\sigma}$. Show that there exists a real $\mu$ such that $\mathcal{F}\left(g_{\sigma}\right) = \mu g_{\sigma^{\prime}}$. The value of $\mu$ need not be made explicit.