Construction of a self-adjoint dilatation for a problem with impedance boundary condition

We study the spectral problem
$$ \Delta u+k^2u=0,\quad\dfrac{\partial u}{\partial n}-ik\sigma u|_{\delta\Omega}=0,\quad\sigma\geqslant0. $$
We construct a self-adjoint dilatation and the problem is reduced to the investigation of a dissipative operator in a space with energy metric.