On the pseudospectra of Schrödinger operators on Zoll manifolds

We consider non-self-adjoint Schrödinger operators Δ + V \Delta +V where Delta"> encoding="application/x-tex">\Delta is the Laplace-Beltrami operator on a Zoll manifold alttext="upper X"> X encoding="application/x-tex">X and V element-of C Superscript normal infinity Baseline left-parenthesis X comma double-struck right-parenthesis"> ∈ C mathvariant="normal">∞<!-- ∞ </mml:msup> ( , mathvariant="double-struck">C stretchy="false">) encoding="application/x-tex">V\in C^\infty (X,\mathbb {C}) . obtain asymptotic results pseudo-spectrum numerical range of such operators.