On the stability in Ambarzumian theorems. (30th January 2015) - Horváth, Miklós
Abstract: We provide extensions of the classical Ambarzumian theorem for bounded C 3 domains of any dimension. The simple proof is based on classical spectral function asymptotics. We prove a stability property by showing that if the perturbation of the eigenvalues of the zero potential is small in some sense then the L 2 -norm of the potential is also small. The problem is motivated by connections to a number of applications.