A uniqueness theorem for the inverse problem for the integrodifferential electrodynamics equations

The problem of finding a kernel and the index of dielectric permeability for the system of integro-differential equations of electrodynamics with wave dispersion is studied. We consider a direct problem in which the external pulse current is a dipole located at a point $y$ on the boundary $\partial B$ of the unit ball $B$. The point $y$ runs over the whole boundary and is a parameter of the problem. The information available about the solution to the direct problem is the trace on $\partial B$ of the solution to the Cauchy problem given for the time moments close to the time when a wave from the dipole source arrives at the point $x$. The main result is a uniqueness theorem for the solution of the inverse problem.