Series index on $\mathbb Z^n$..

Series index on $\mathbb Z^n$..

does anyone know if there is a book that deal with series of the kind,
$$\displaystyle \sum_{\xi\in\mathbb Z^n}a_\xi,$$ that is, when the indices
are in the space $\mathbb Z^n$. I'm looking for the theory of convergence
of these series.. Thanks