  We explore the mathematical theory to rigorously describe the response of
media with linear time-varying, generally dispersive, electromagnetic
constitutive parameters. We show that even when the temporal inhomogeneity
takes place on a time scale comparable or shorter than the driving fields' time
period, one can still define a physically meaningful time-varying dispersion.
Accordingly, a generalized set of Kramers-Kronig relations is investigated to
link the real and imaginary parts of the time-varying frequency-dispersive
spectra characterizing the medium's constitutive response. Among others, we
study the case of a Lorentzian dielectric response with time-varying volumetric
density of polarizable atoms and present the varying circuital equivalents of
the governing differential equation, which in turn allow us to use the notion
of generalized time-varying impedances/admittances of a time-dependent
resistor, inductor and capacitor.
