It is known that for each integrable function $f:[-\pi,\pi] \to \Bbb C$, with fourier coefficients $a_n$ ($n \in \Bbb Z$),
$$ (1) \sum_{n=-\infty}^\infty |a_n|^2 <\infty$$ My question is This:Given a sequence of complex numbers $a_n$ such that (1) holds, Is it always possible to find an integrable function $f$ such that $a_n$ are its Fourier coefficients? If not, what conditions are sufficent for an existence of such function?