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.

Keywords:

• Dirac equations
• jump condition
• eigenparameter boundary condition
• uniqueness theorem

AMS Subject Classifications:

• 34A55
• 34B24
• 34L05

Acknowledgements

The author would like to thank the referees for valuable comments. The author is indebted to Professor V.A. Yurko and Professor S.A. Buterin for stimulating discussions concerning spectral analysis of differential operators.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the National Natural Science Foundation of China [11171152] and Natural Science Foundation of Jiangsu Province of China [BK 2014021904].