Recall that a function $f: \mathbb{R} \longrightarrow \mathbb{C}$ is positive definite, iff for all numbers $N$ and $x_1, \dots, x_N \in \mathbb{R}$, the matrix $(a_{ij})$ with the entries
$$a_{ij} = f(x_i - x_j)$$
is positive semi-definite.

My question is: Let $g \in L^2(\mathbb{R}^n)$. Is the function
$$f(z, y) =\int_{\mathbb{R}^n} g(x - y) \overline{g(x-z)} d x$$
positive definite on $\mathbb{R}^{2n}$?