On the Complex Symmetry of the Poincaré-steklov Operator

Employing Lorentz reciprocity and the Stratton-Chu formalism it is shown that the Poincaré-Steklov or admittance operator can be interpreted as a complex symmetric operator mapping the tangential electric field (instead of the equivalent magnetic current) onto the equivalent electric current. We show that the pertinent block Calderón projectors can be reformulated as operators with a block Hamiltonian structure. This leads to an explicitly complex symmetric Schur complement expression for both the interior and exterior admittance operators.