Functional Model of Dissipative Fourth Order Differential Operators

Abstract

In this paper, maximal dissipative fourth order operators with equal deficiency indices are investigated. We construct a self adjoint dilation of such operators. We also construct a functional model of the maximal dissipative operator which based on the method of Pavlov and define its characteristic function. We prove theorems on the completeness of the system of eigenvalues and eigenvectors of the maximal dissipative fourth order operators.

Keywords

• dilation
• dissipative operator
• completeness of the system of eigenvectors and associated vectors
• scattering matrix
• functional model
• characteristic function