Spectral analysis for one class of second-order indefinite non-self-adjoint differential operator pencil

摘要

The inverse problem for the differential operator pencil with complexperiodic potential and discontinuous coefficients on the axis is studied. Maincharacteristics of the fundamental solutions are investigated, the spectrum ofthe operator is studied. We give formulation of the inverse problem, prove auniqueness theorem and provide a constructive procedure for the solution of theinverse problem