Impedance boundary condition and extensions of the Maxwell operator

The von Neumann theory of selfadjoint extension of symmetric operators used here for constructing a nonselfadjoint in general closed extension, corresponding to impedance boundary value problem for the Maxwell equation. Deficiency spaces of corresponding operator A^S ₀ are presented as a space Lfr of pairs of linear differential forms distributions on the boundary surface S. So the problem of constructing the operator connecting deficiency spaces and defining the closed extensions is reduced to the inversion problem for a pseudodifferential operator acting in the space Lfr and depending on the impedance operator on a space of linear differential forms distributions on the boundary surface S