Gevrey-Type Resolvent Estimates at the Threshold for a Class of Non-Selfadjoint Schrödinger Operators

In this article, we show that under some coercive assumption on the complexvalued potential V (x), the derivatives of the resolvent of the non-selfadjint Schröinger operator H = −∆ + V (x) satisfy some Gevrey estimates at the threshold zero. As applications, we establish subexponential time-decay estimates of local energies for the semigroup e−tH , t > 0. We also show that for a class of Witten Laplacians for which zero is an eigenvalue embedded in the continuous spectrum, the solutions to the heat equation converges subexponentially to the steady solution.