Bochner's theorem (for the real line version) asserts an infinite tower of inequalities, as a positivity condition. Taking each one, what do they mean, in an elementary fashion (at least at the start)?

For instance, the $1 \times 1$ matrix says that $Q(0)$ is positive. The $2 \times 2$ says that $|Q(x)| \ge |Q(0)|$. (And these two are commonly written down for necessary conditions of characteristic functions.) What about 3 and 4?

fixedn? So I think your $f$ is Wikipedia's $Q$? – Matthew Daws Apr 26 '12 at 13:40