Some Properties of Eigenvalues and Generalized Eigenvectors of One Boundary Value Problem

Abstract

We investigate a discontinuous boundary value problem which consists
of a Sturm-Liouville equation with piecewise continuous potential
together with eigenparameter-dependent boundary conditions and
supplementary transmission conditions. We establish some spectral
properties of the considered problem. In particular it is shown that
the generalized eigenfunctions form a Riesz basis of the adequate
Hilbert space.