Stability of Direct and Inverse Eigenvalue Problems for Schrodinger Operators on Finite Intervals

Abstract

We consider the inverse eigenvalue problem for Schrödinger operators on finite intervals. Among others, we show that if the potential is in Lp, then the perturbation of the potentials can be estimated by the lp′-norm of the sequence of the eigenvalue differences only if p ≥ 2. As a consequence, we give estimates if only finite number of eigenvalues are known with an error < ε.