Counting eigenvalues of Schrödinger operators with fast decaying complex potentials

Abstract We give a sharp estimate of the number of zeros of analytic functions in the unit disc belonging to analytic quasianalytic Carleman–Gevrey classes. As an application, we estimate the number of the eigenvalues for discrete Schrodinger operators with rapidly decreasing complex-valued potentials, and, more generally, for non-symmetric Jacobi matrices.