On spectral properties of dissipative fourth order boundary-value problem with a spectral parameter in the boundary condition

In this article, we consider dissipative fourth order boundary-value problem in the Lim-4 case with the spectral parameter in the boundary condition. We use the maximal dissipative operator to construct a self-adjoint dilation of this operator and its incoming and outgoing spectral representations. Then, we determine the scattering matrix of dilation. We also construct a functional model of the maximal dissipative operator and define its characteristic function in terms of solutions of the corresponding fourth order equation. Theorem on the completeness of the system of eigenvector and associated vectors of this operator are proved.