Determination of Dirac operator with eigenparameter-dependent boundary conditions from interior spectral data

In this article, inverse spectra problems for Dirac operator with eigenparameter-dependent boundary conditions are studied. By using the approach similar to those in Hochstadt and Lieberman [H. Hochstadt and B. Lieberman, An inverse Sturm-Liouville problem with mixed given data, SIAM J. Appl. Math. 34 (1978), pp. 676-680] and Ramm [A.G. Ramm, Property C for ODE and applications to inverse problems, Operator theory and applications, Vol. 25, AMS, Providence, RI, 2000, pp. 15-75], we prove that (1) a set of values of eigenfunctions at the midpoint of the interval [0, 1] and one spectrum suffice to determine the potential Q(x) on the interval [0, 1] and all parameters in the boundary conditions; (2) some information on eigenfunctions at an internal point b is an element of (1/2, 1) and parts of two spectra suffice to determine the potential Q(x) on the interval [0, 1] and all parameters in the boundary conditions.