Methods for verifying solvability of the permittivity reconstruction in canonical waveguide inverse problems

We present a summary of mathematical methods that enable one to study and reveal the properties of the transmission coefficient as a function of problem parameters aimed at solution to some canonical waveguide inverse problems. The results are based on application of the theory of functions of several complex variables and singularities of differentiable mappings and lead to substantial improvement of the available techniques for permittivity reconstruction of material samples in waveguides.