Let $f,g: \mathbb{R} \to \mathbb{C}$ $2\pi$ periodic , Riemann integrable in $[0, 2\pi]$. I need to prove that if $f(x)=0$ for every $x$ around $x_0$ so $S_nf(x_0) \to 0$ when $n \to \infty$.
We define $S_nf(x_0)=\sum_{-n}^{n}\hat f(n)e^{inx_o}$ and $\hat f(n)=
Thank you very much