On the solvability of an inverse problem in the central symmetric case

Abstract

An inverse problem of spectral analysis is studied for Sturm–Liouville differential operators with non-separated boundary conditions. For the central symmetric case, we prove the local solvability of the inverse problem of recovering the potential from one spectrum.

Keywords:

• Sturm–Liouville operators
• inverse spectral problems
• local solvability

AMS Subject Classifications::

• 34A55
• 34B24
• 47E05

Acknowledgements

This research was supported in part by DAAD, by Qatar National Research Fund (project NPRP 08-345-1-067), by Russian Foundation for Basic Research and Taiwan National Science Council (projects 10-01-00099 and 10-01-92001-NSC).