The Characterization Of Self-adjoint Domain Of Two Interval Vector Differential Operator

In this paper,we mainly study the self-adjoint extension problem of two-interval vector differential operators,according to a theory of self-adjoint realizations of Sturm-Liouville problems on two intervals in the direct sum of Hilbert spaces associated with these intervals.In this paper,first of all,we give a complete characterization of self-adjoint ex-tensions of the two-interval minimal operator of Sturm-Liouville vector differential operators in terms of Sturm-Liouville vector differential equation solutions of the two intervals.This result reduces to the case when one or two or three or four endpoints are regular.Secondly,we give a characterization of all self-adjoint extensions of the two-interval minimal operator of vector differential operators with one endpoint of each interval is singular and each endpoint of two intervals is singular on two intervals in the direct sum of Hilbert spaces in terms of vector differential equation solutions.