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

Abstract

The inverse problem for the Schrodinger operator with complex periodic potentials and discontinuous coefficient on the axis is studied. Main characteristics of the fundamental solutions are investigated, the spectrum of the operator is analysed. The inverse problem is formulated, a uniqueness theorem is proved, a constructive procedure for the solution of the inverse problem is provided.

Keywords:

• discontinuous equation
• spectral singularities
• inverse spectral problem
• continuous spectrum

AMS Subject Classifications::

• 34A36
• 34L05
• 47A10
• 47A70

Acknowledgments

The author to thanks the referees whose comments helped to improve the presentation of this article.