Time-domain Fresnel´s formulas for a plane interface between media

The time-domain operators are obtained that allow one to describe a transformation of an arbitrary initial field by a flat interface between two media in the 3-D case. The medium in one of the two halfspaces changes its permittivity and acquires a conductivity. The description includes a case when a boundary is created at some moment of time. Transmitted and reflected signals are determined by integral operators that take into account the field polarisation characteristics. Weight factors in kernels of these operators are just analogues of Fresnel formulae. The obtained resolvent consists of two parts the first of which is a mere generalisation of a resolvent for an unbounded medium and the second occurs through availability of an interface between media