M. Lassas, INVERSE BOUNDARY SPECTRAL PROBLEM FOR NONSELF-ADJOINT MAXWELLS EQUATIONS WITH INCOMPLETE DATA, Communications in partial differential equations, 23(3-4), 1998, pp. 629-648
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.