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

Abstract

In this article, we show that under some coercive assumption on the complex-valued potential V(x), the derivatives of the resolvent of the non-selfadjoint 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.

Keywords

• Gevrey estimate of resolvent
• threshold spectral analysis
• non-selfadjoint Schrödinger operators
• Witten Laplacian