A Half-Inverse Problem for Impulsive Dirac Operator with Discontinuous Coefficient

Abstract

An inverse problem for Dirac differential operators with discontinuity conditions and discontinuous coefficient is studied. It is shown by Hochstadt and Lieberman's method that if the potential function $p(x)$ in $\Omega (x)$ is prescribed over the interval $(\pi /2,\pi )$, then a single spectrum suffices to determine $p(x)$ on the interval $(0,\pi )$ and it is also shown here that $\rho (x)$ is uniquely determined by a spectrum.