A partial inverse problem for the Sturm-Liouville operator on a star-shaped graph (Q1743914)

Inverse problem of spectral analysis is studied for Sturm-Liouville operators on star-shaped graphs. It is proved that the specification of a part of the spectrum uniquely determines the potential on one edge provided that the potential on the remaining edges are known a priori. An algorithm for constructing the solution for this inverse problem is suggested, and stability of the solution is established.