Coordinate-Free Approach for the Characteristic Function of a Fourth-Order Dissipative Operator

Abstract

In this article, we investigate some spectral properties of a singular dissipative fourth-order dissipative operator in case at the singular point. For this purpose we construct the characteristic function of both maximal simple dissipative operator and completely non-unitary contraction which is the Cayley transform of the dissipative operator. Using the properties of the characteristic operator-function we obtain the related results of the boundary value problem. Moreover we obtain the selfadjoint dilation of the maximal dissipative operator and its incoming and outgoing eigenfunctions by using coordinate-free approach.