Isoresonant Complex-valued Potentials and Symmetries

Abstract

Abstract Let X be a connected Riemannian manifold such that the resolvent of the free Laplacian , has a meromorphic continuation through . The poles of this continuation are called resonances. When X has some symmetries, we construct complex-valued potentials, V, such that the resolvent of, which has also ameromorphic continuation, has the same resonances with multiplicities as the free Laplacian.