Hochstadt–Lieberman theorem for Dirac operator with eigenparameter dependent boundary conditions

Abstract

We consider an inverse problem for the Dirac operator with the spectral parameter in the boundary conditions. In this work, using Hochstadt and Lieberman’s method (Hochstadt and Lieberman (1978) [1]) we show that if the potential Q(x) is prescribed on the half interval [12,1], then a single spectrum of the Dirac operator with eigenparameter dependent boundary conditions on the whole interval [0,1] suffices to determine Q(x) on another half-interval [0,12], and the boundary condition at x=0.