Let $\sum^{\infty}_{-\infty} |d_n| < \infty$ and define $f(x):= \sum^{\infty}_{-\infty} d_n e^{inx}$ for $x \in \mathbb R$.
Find the Fourier series for $f$ and show it converge uniformly on $\mathbb R$ aswell on $L^2$ against $f$.
How can I start on this exercise ? First of all I must determine $f$ ? - but this series is not an ordinary series ?
Secondly, I have the Fourier series of $f$ is defined as $$\sum_{-\infty}^{\infty} \frac 1 {2\pi} (\int^{\pi}_{-\pi} f(y) e^{-iny} dy)e^{inx}$$, but in order to compute this I must know the integral ?