Approximating eigenvalues of discontinuous problems by sampling theorems

We use sampling techniques to compute eigenvalues of discontinuous second order boundary value problems. The eigenvalues are in general complex numbers and are not necessarily simple. Therefore error estimates for the truncation and amplitude errors on C of the sampling expansion and its termwise derivative are used. Moreover the problem we consider has two parts throughout [-1,1] and is not in general self adjoint. The boundary and compatibility conditions are assumed to be regular in the sense of Birkhoff to guarantee the existence of eigenvalues.