INVERSE BOUNDARY SPECTRAL PROBLEM FOR NONSELF-ADJOINT MAXWELLS EQUATIONS WITH INCOMPLETE DATA

The inverse boundary spectral problem for selfadjoint Maxwell's equati ons is to reconstruct unknown coefficient functions in Maxwell's equat ions from the knowledge of the boundary spectral data, i.e., from the eigenvalues and the boundary values of the eigenfunctions. Since the s pectrum of non-selfadjoint Maxwell's operator consists bf normal eigen values and an interval, the complete boundary spectral data can be def ined only in a very complicated way. In this article we show that the coefficients can be reconstructed from incomplete data, that is, from the large eigenvalues and the boundary values of the generalized eigen functions. Particularly, we do not need the infinite-dimensional data corresponding to the non-discrete spectrum.