Stability for the inverse resonance problem for a Jacobi operator with complex potential

The potential of a discrete half-line Schrodinger operator is uniquely determined by the location of its Dirichlet eigenvalues and resonances. In a practical setting one can expect only to know a finite number of these. In this paper we give an estimate for the difference of two potentials (one of them finitely supported) for which eigenvalues and small resonances are the same but which may differ with respect to their large resonances.