Inverse problems for differential operators on trees with general matching conditions

Abstract

Sturm–Liouville differential operators on compact trees with general matching conditions in internal vertices are studied. We establish properties of the spectral characteristics and investigate three inverse problems of recovering the operator either from the so-called Weyl functions, or from discrete spectral data or from a system of spectra. For these inverse problems, we prove the corresponding uniqueness theorems and obtain procedures for constructing their solutions by the method of spectral mappings.

Keywords:

• Sturm–Liouville equations on graphs
• Inverse spectral problems
• Method of spectral mappings
• AMS Classifications:
• 34A55
• 34B45
• 34L05
• 47E05

Acknowledgement

This research was supported in part by Grant 04-01-00007 of Russian Foundation for Basic Research.