THE LIPSCHITZ STABILITY OF INVERSE NODAL PROBLEM FOR DIRAC SYSTEM

Abstract

Inverse nodal problem on Dirac operator is determination problem of the parameters in the boundary conditions, number m and potential function V by using a set of nodal points of a component of two component vector eigenfunctions as the given spectral data. In this study, we solve a stability problem using nodal set of vector eigenfunctions and show that the space of all V functions is homeomorphic to the partition set of all space of asymptotically equivalent nodal sequences induced by an equivalence relation. Moreover, we give a reconstruction formula for the potential function as a limit of a sequence of functions and associated nodal data of one component of vector eigenfunction. Our technique depends on the explicit asymptotic expressions of the nodal parameters and, it is basically similar to [1, 2] which is given for Sturm-Liouville and Hill's operators, respectively.