Investigation of the Eigenvalues and root functions of the boundary value problem together with a transmission matrix

Abstract

In this paper, we consider a singular even-order Hamiltonian system on the union of two intervals together with appropriate boundary and  transmission conditions. For investigating the spectral properties of the problem we pass to the inverse operator with an explicit form and we prove some completeness theorems.

Mathematics Subject Classication (2010): Primary: 30E25, 34B20; Secondary: 35P10.

Key words: Hamiltonian system, spectral analysis, transmission condition.