Transmission eigenvalue problems in electromagnetics and the principle of causality

Transmission 'eigenvalue' problems arise in connection with the non destructive testing and in the imaging of a material body by means of electromagnetic waves. The equations of electromagnetic waves rely on the finiteness of c and imply the principle of causality. Compliance with this principle has a counterpart in the model of the material media and is formalised by the KRAMERS-KRONIG relations. The spectral theory of some extensively studied elliptic transmission problems which involve wavenumber-independent (i.e., non causal) material properties, is physically inconsistent. Therefore, the open problems motivated herewith are: 1) how to bring in KRAMERS-KRONIG-compliant material parameters (not just permittivity), 2) accordingly, prove or disprove the existence of real eigenvalues, 3) formalise an approximation theory, 4) address material resonances.