Dissipative Sturm-Liouville operators with a spectral parameter in the boundary condition on bounded time scales

Abstract

In this article we consider a second-order Sturm-Liouville operator with a spectral parameter in the boundary condition on bounded time scales. We construct a selfadjoint dilation of the dissipative Sturm-Liouville operators. Using by methods of Pavlov [40,41,42], we prove the completeness of the system of eigenvectors and associated vectors of the dissipative Sturm-Liouville operators on bounded time scales.

Keywords

• Time scale
• delta-differentiable
• dilation
• dissipative operator
• system of eigenvectors
• scattering matrix
• functional model
• characteristic function