Monthly Archives: December 2017

Let $\hat f(n) = \frac{1}{2\pi} \int_{-\pi}^\pi f(t)e^{-int} \, \text{d}t$ be the Fourier coefficients of $f$. Theorem. $\hat f(n) = 0$ implies $f(t) = 0$ when $f$ is continuous at $t$. Proof. By linearity, this is equivalent to showing that $\hat … Continue reading →