Eigenvalues of Schr\"odinger operators with complex surface potentials

Abstract

We consider Schr\"odinger operators in $\mathbb R^d$ with complex potentials supported on a hyperplane and show that all eigenvalues lie in a disk in the complex plane with radius bounded in terms of the $L^p$ norm of the potential with $d-1<p\leq d$. We also prove bounds on sums of powers of eigenvalues.