OPERATOR-PENCIL REALIZATION OF ONE STURM-LIOUVILLE PROBLEM WITH TRANSMISSION CONDITIONS

Abstract

We consider a class of boundary value problems on two disjoint intervals for Sturm-Liouville equation together with supplementary transmission conditions at the point of interaction. The spectral parameter lambda appears not only in the Sturm-Liouville equation but also in the boundary conditions. We construct an operator-pencil formulation of these boundary value problems and investigate their spectral properties. In particular we define the generalized eigenfunctions and establish that the spectrum of the considered problem is discrete and the set of generalized eigenfunctions form a basis of the corresponding Hilbert space.