Representation of All Maximally Dissipative Multipoint Differential Operators for First Order

Abstract

In this work, we consider the linear multipoint symmetric differential-operator expression for first order in the Hilbert space of vector functions defined on the left hand and right hand semi-axis. The minimal and maximal operators corresponding to this differential-operator expression are constructed. For the minimal symmetric operator, deficiency indices are computed and the triplet of boundary values is determined. Later on, the general form of maximally dissipative extensions of the minimal operator generated by considered differential-operator expression has been obtained with the use of the Calkin-Gorbachuk method. Furthermore the structure of spectrum of these type extensions is investigated. Finally, we provide an application which supports our results.