Some Ambarzumyan-type theorems for Dirac operators

Abstract

Ambarzumyan's theorem describes the exceptional case in which the spectrum of a single Sturm–Liouville problem with the Neumann boundary conditions on a finite interval uniquely determines the potential. In this paper, the result of Ambarzumyan is extended to many-dimensional Dirac operators with quasi-periodic boundary conditions. We also extend some results of the previous work (Yang C-F and Huang Z-Y 2007 Inverse Problems 23 2565–74).