Let $C$ be a quadratic functional operator of single variable. For example: $C(u)=u^{2}(t)$. The notation $dC$ means Frechet derivative. Although I know that $d^{2}C$ would be a constant since $C$ is quadratic, what does it mean for the following notation?
$$d^{2}C[f,g]$$
An author stated that the above is constant for quadratic $C$.