Monthly Archives: July 2018

Statement. $F[e^{-\pi x^2}] = e^{-\pi x^2}$ Proof. $$ \begin{eqnarray} F[e^{-\pi x^2}](s) &=& \int_{\Bbb R} e^{-\pi x^2} e^{-2\pi i sx} dx \\ &=& \int_{\Bbb R} e^{-\pi x^2 -2\pi i sx} dx \\ &=& e^{\pi (is)^2} \int_{\Bbb R} e^{-\pi x^2 -2\pi i sx – … Continue reading →