= Positive-definite function
{title2=$\sum_{i,j}z_i\overline{z_j}p(x_i x_j^{-1})\geq0$}
{wiki}
A complex-valued function on a group is positive-definite when the displayed inequality holds for every finite choice of points and coefficients. This includes positive semidefinite, rather than necessarily strictly positive definite, Gram matrices. In particular $p(e)\geq0$ and $|p(x)|\leq p(e)$. On an Abelian group, every convolution square $u*u^*$ with $u\in C_c(G)$ is continuous and positive-definite: its quadratic form is the integral of $|\sum_i z_i u(t+x_i)|^2$.
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