Inverse problems for Dirac equations polynomially depending on the spectral parameter

Abstract

Inverse spectral problems are considered for Dirac equations with boundary conditions depending polynomially on the spectral parameter and with a transmission condition. We give formulations of the associated inverse problems such as Titchmarsh–Weyl theorem, and prove corresponding uniqueness theorems. Using Titchmarsh–Weyl theorem, we also obtain two analogues of a theorem of Hochstadt–Lieberman and a theorem of Mochizuki–Trooshin for this kind of Dirac operators. The obtained results are generalizations of the similar results for the classical Dirac operator.