Inverse Spectral Theory and Kramers-Kronig Relations (contributed talk)

Inverse problems aimed at locating cracks and voids inside a dielectric medium by means of electromagnetic waves involve knowledge of transmission eigenvalues. The subject has been actively investigated by many Authors for some years and results have been presented in articles and books. Unfortunately, the frequency dependence of dielectric permittivity and magnetic permeability of the material has not been taken into account. A theorem which provides existence and asymptotic properties of real transmission eigenvalues is shown to be physically inconsistent, because it ignores the Kramers-Kronig relations.