Hi, if the Fourier series development of $g(t)$ (periodic, $C^\infty$) is

$$ g(t)=\sum_{-\infty}^{+\infty}a_n e^{in\omega t} $$

does the series

$$ \sum_{-\infty}^{+\infty}\frac{a_n^2}{n^2}? $$ converges toward something known like average $g^2$ or something like that?