Sum rules can be derived using properties of Herglotz functions. Typically, they can be put in the form of physical bounds in the frequency domain, as the product of a performance metric (for instance, minimum extinction cross section) and bandwidth being limited by the static polarizability of the scatterer. In this talk, we will see how the sum rule can also, at least in some cases, be interpreted in the time domain, as a moment of the impulse response, corresponding to the average delay of the system.