Self-adjoint Sturm-liouville Operator. Multi-interval Sub-and High-order Ordinary Differential Operator Eigenvalue Multiplicity Relationship

In this paper,we discuss the relationship between the analytic and geometric multiplicities of an eigenvalue of a self-adjoint ordinary differential operator.First of all, we prove the equality between analytic and geometric multiplicities of an eigenvalue of a self-adjoint multi-interval Sturm-Liouville problem,which is an analogue to the case of the regular Sturm-Liouville problem.Then,using the same method,we prove the equality of multiplicities of a self-adjoint high-order ordinary differential operator.