Spectral properties of boundary-value problem with a shift for wave equation

Abstract

We consider a differential operator determined by wave equation with potential in characteristic triangle, and boundary-value conditions with shift on the characteristics, and with oblique derivative on non-characteristic part of a boundary. We obtain condition for validity of the Volterra property, and show completeness of the root functions in the rest cases. We study basis property for the system of root functions under assumption that the potential depends on a single variable.