If $ \sum_{k=-\infty}^{\infty} |\hat f (k) | < \infty $ does it implies $ S_n(t)=\sum_{k=-n}^{n} \hat f (k) e^{ikt} \to f(t) \; ? $
I know $S_n$ converges for each $t$ to some function $S$.
Can we say that $S$ is equal to $f$?
From what I read in our book (Katznelson), it's not clear for me.