Open Access Research

Inverse spectral problems for non-selfadjoint second-order differential operators with Dirichlet boundary conditions

Sergey A Buterin1, Chung-Tsun Shieh2* and Vjacheslav A Yurko1

Author Affiliations

1 Department of Mathematics, Saratov State University, Astrakhanskaya str. 83, Saratov, 410012, Russia

2 Department of Mathematics, Tamkang University, Tamsui, New Taipei, 25137, Taiwan

For all author emails, please log on.

Boundary Value Problems 2013, 2013:180  doi:10.1186/1687-2770-2013-180

Published: 6 August 2013

Abstract

We study the inverse problem for non-selfadjoint Sturm-Liouville operators on a finite interval with possibly multiple spectra. We prove the uniqueness theorem and obtain constructive procedures for solving the inverse problem along with the necessary and sufficient conditions of its solvability and also prove the stability of the solution.

MSC: 34A55, 34B24, 47E05.

Keywords:
non-selfadjoint Sturm-Liouville operators; inverse spectral problems; method of spectral mappings; generalized spectral data; generalized weight numbers