An Isaac Newton Institute Workshop

Quantum Graphs, their Spectra and Applications

Inverse spectral problems on compact and noncompact trees

Authors: Gerhard Freiling (Universitaet Duisburg), Vjacheslav Yurko (Saratov University)

Abstract

Second-order differential operators on compact or noncompact trees with standard or general mathching conditions in internal vertices are studied. We establish properties of the spectral characteristics and investigate the inverse problem of recovering the operator from the so-called Weyl vector. For this inverse problem we prove a uniqueness theorem and provide a procedure for constructing the solution.