Determination of the Impulsive Dirac Systems from a Set of Eigenvalues

In this work, we consider the inverse spectral problem for the impulsive Dirac systems on (0,pi) with the jump condition at the point pi/2. We conclude that the matrix potential Q(x) on the whole interval can be uniquely determined by a set of eigenvalues for two cases: (i) the matrix potential Q(x) is given on (0,(1+alpha)pi/4); (ii) the matrix potential Q(x) is given on ((1+alpha)pi/4, pi), where 0 < alpha < 1.

Automated summary

This work focuses on the inverse spectral problem for impulsive Dirac systems with jump conditions at a specific point on the interval (0, pi), and concludes that the matrix potential can be uniquely determined based on a set of eigenvalues under certain conditions.