Functional model for generalised resolvents and its application to time-dispersive media

Abstract

Motivated by recent results concerning the asymptotic behaviour of differential operators with highly contrasting coefficients, whose effective descriptions have involved generalised resolvents, we construct the functional model for a typical example of the latter. This provides a spectral representation for the generalised resolvent, which can be utilised for further analysis, in particular the construction of the scattering operator in related wave propagation setups.