On the pseudospectra of Schrödinger operators on Zoll manifolds

Abstract

We consider non-self-adjoint Schrödinger operators Δ + V \Delta +V where Δ \Delta is the Laplace-Beltrami operator on a Zoll manifold X X and V ∈ C ∞ ( X , C ) V\in C^\infty (X,\mathbb {C}) . We obtain asymptotic results on the pseudo-spectrum and numerical range of such operators.