Extensions of a Minimal Third-Order Formally Symmetric Operator

Abstract

In this paper, we consider some regular boundary value problems generated by a third-order differential equation and some boundary conditions. In particular, we construct maximal self-adjoint, maximal dissipative and maximal accumulative extensions of the minimal operator. Further using Lax–Phillips scattering theory and Sz.-Nagy–Foias characteristic function theory we prove a completeness theorem.