Gelfand-Levitan condition for Dirac operators

We discuss how to generalize a Dirac operator such that the solution of a Dirac equation is of bounded variation rather than continuous. We build the spectral theory for generalized Dirac operators and discuss the connection between them and canonical systems. With the help of de Branges' theory, we discuss the de Branges space of such an operator and the norm endowed. On the other hand, the Paley-Wiener theorem gives us a chance to recover a Dirac operator from a function that plays the same role as the spectral measure, which is well-known as the Gelfand-Levitan condition.