Lemma 32.4.3.label Let $G$ be a locally compact group and $\phi \in BC(G; \complex)$ be a positive-definite function, then $\ol \phi$ is also positive definite.
Proof, [Proposition 3.14, Fol16]. For any $f \in L^{1}(G; \complex)$,
\[\int_{G} (f^{*} * f)\ol \phi = \int_{G} (\ol{f}^{*} * \ol{f}) \phi\]
$\square$
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