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An interior inverse problem for the impulsive Dirac operator. (English) Zbl 1242.34028
The authors study the Dirac system $$ By'+\Omega(x)y=\lambda y,\quad 0<x<\pi, $$ $$ y=\left[ \matrix y_1 \\ y_2 \endmatrix\right],\quad B= \left[ \matrix 0 & 1 \\ -1 & 0 \endmatrix\right],\quad \Omega(x)= \left[ \matrix p(x) & q(x) \\ q(x) & p(x) \endmatrix\right], $$ with discontinuous conditions inside the interval and with boundary conditions $$ y_1(0)=0,\quad y_2(\pi)=0. $$ The inverse problem of recovering $p(x)$ from the so-called interior spectral data is studied, provided that $q(x)$ are known a priori. For this inverse problem a uniqueness theorem is proved.

34A55Inverse problems of ODE
34B24Sturm-Liouville theory
34L05General spectral theory for OD operators
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