# How to show that $g^**g$ is a function of positive type, $g \in L^1(G) \cap L^2(G)$?

Let $$G$$ be a locally compact abelian Hausdorff group (with Haar measure $$d\mu$$). Call a function $$h \in L^\infty(G)$$ a function of positive type if $$\int_G (f^* *f)h \, d\mu \geq 0 \ \ \ \forall f \in L^1(G) \ \ \ \ \ \ (\#)$$

where $$f^*(x) := \overline{f(x^{-1})}$$ denotes the involution.

Now let $$g \in L^1(G) \cap L^2(G)$$. I want to show that $$h := g^**g$$ is of positive type. Clearly $$h \in L^\infty(G)$$ by Cauchy Schwarz but I have trouble to show the property $$(\#)$$.