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.
@article{5891,
title = {Gevrey-Type Resolvent Estimates at the Threshold for a Class of Non-Selfadjoint Schr\"odinger Operators},
journal = {Bruno Pini Mathematical Analysis Seminar},
year = {2015},
doi = {10.6092/issn.2240-2829/5891},
language = {EN},
url = {http://dml.mathdoc.fr/item/5891}
}
Wang, Xue Ping. Gevrey-Type Resolvent Estimates at the Threshold for a Class of Non-Selfadjoint Schrödinger Operators. Bruno Pini Mathematical Analysis Seminar, (2015), . doi : 10.6092/issn.2240-2829/5891. http://gdmltest.u-ga.fr/item/5891/