Generator square inequality
= Generator square inequality
{title2=$L(f^2)\geq2fLf$}
If real $f$ and $f^2$ belong to the <generator domain> of a <Feller semigroup>, <Jensen inequality> gives $P_t(f^2)-(P_tf)^2\geq0$. This expression is zero at $t=0$, so its right <derivative> is nonnegative, proving the inequality. It is equivalent to <positivity> of the <carré du champ>.