Monthly Archives: March 2018

Theorem. Suppose $\lim_{|z|\to\infty} |f(z)| = 0$ and $a > 0$. Then $\lim_{R\to \infty} \int_{C_R} e^{iaz} f(z) \, dz = 0$ where $C_R$ is the semicircle in the upper half-plane with radius $R$ centered on $0$. Proof. Our assumption implies that … Continue reading →