Determination of Dirac operator with eigenvalue-dependent boundary and jump conditions

Abstract

Dirac operator with eigenvalue-dependent boundary and jump conditions is studied. Uniqueness theorems of the inverse problems from either Weyl function or the spectral data (the sets of eigenvalues and norming constants except for one eigenvalue and corresponding norming constant; two sets of different eigenvalues except for two eigenvalues) are proved. Finally, we investigate two applications of these theorems and obtain analogues of a theorem of Hochstadt-Lieberman and a theorem of Mochizuki-Trooshin.

Keywords:

• Dirac operator
• inverse problem
• jump condition
• eigenparameter boundary condition
• missing eigenvalue

AMS Subject Classifications:

• 34A55
• 34B24
• 34L05

Notes

1 This research was supported by the National Natural Science Foundation of China (11171152).