Inverse spectral problems for differential operators on spatial networks

Abstract

A short survey is given of results on inverse spectral problems for ordinary differential operators on spatial networks (geometrical graphs). The focus is on the most important non-linear inverse problems of recovering coefficients of differential equations from spectral characteristics when the structure of the graph is known a priori. The first half of the survey presents results related to inverse Sturm–Liouville problems on arbitrary compact graphs. Results on inverse problems for differential operators of arbitrary order on compact graphs are then presented. In the conclusion the main results on inverse problems on non-compact graphs are given. Bibliography: 55 titles.