Let $f \in C[−\pi, \pi]$. Show that both the n-th Fourier sine and the n-th Fourier cosine coefficients of $f$ go to $0$ as $n \to +\infty$.
Hello guys. I did some work for proof but I am not sure that I am on the right track. I used Bessel's inequality and got that $\left\Vert f \right\Vert ^2 ≥ \pi \cdot \sum \left(|a_n|^2 +|b_n|^2 \right)$.
How should i continue?