On recovering Sturm—Liouville operators on graphs

Research paper by V. A. Yurko

Indexed on: 01 Mar '06Published on: 01 Mar '06Published in: Mathematical Notes


Sturm—Liouville differential operators on compact graphs are studied. We establish properties of the spectral characteristics and investigate three inverse problems of recovering the operator from the so-called Weyl functions, from discrete spectral data, and from a system of spectra. For these inverse problems, we prove uniqueness theorems and obtain procedures for constructing the solutions by the method of spectral mappings.