Uniqueness theorems for the impulsive Dirac operator with discontinuity (Q2066354)

The paper deals with an impulsive Dirac operator with discontinuity \[ly:=-By^{\prime}+Q(x)y=\lambda\rho y,\qquad x\in(0,\pi),\] with the boundary conditions \[U(y):=y_{1}(0)\cos\alpha+y_{2}(0)\sin\alpha=0,\,\,V(y):=y_{1}(\pi)\cos\beta+y_{2}(\pi)\sin\beta=0\] and the jump conditions \[y_{1}(b+0)=a_{1}y_{1}(b-0),y_{2}(b+0)=a_{1}^{-1}y_{2}(b-0)+a_{2}y_{1}(b-0).\] Here \(\alpha\in(-\pi/2,\pi/2]\) and \(\beta\in(-\pi/2,\pi/2).\) For studying the inverse problem for \(l\), the author introduced the new supplementary data to prove the uniqueness theorems. It is shown that the potential on the whole interval can be uniquely determined by these given data, which are the analogues of Borg, Marchenko and McLaughlin-Rundell theorems. The results in this paper can be viewed as the generalizing in [\textit{T. N. Harutyunyan}, Lobachevskii J. Math. 40, No. 10, 1489--1497 (2019; Zbl 1483.34028)].