# Gevrey estimates of the resolvent and sub-exponential time-decay of solutions

## TL;DR

This paper investigates non-selfadjoint Schrödinger operators, establishing Gevrey estimates for their resolvent derivatives and deriving sub-exponential decay rates for associated semigroups, even with zero eigenvalues or resonances.

## Contribution

It provides new Gevrey estimates for resolvent derivatives of a class of non-selfadjoint Schrödinger operators and analyzes their long-time decay behavior.

## Key findings

- Gevrey estimates hold at zero threshold for the resolvent derivatives.
- Semigroups exhibit sub-exponential decay over time.
- Results include cases with zero eigenvalues and resonances.

## Abstract

In this article, we study a class of non-selfadjoint Schr{\"o}dinger operators H which are perturbation of some model operator H 0 satisfying a weighted coercive assumption. For the model operator H 0 , we prove that the derivatives of the resolvent satisfy some Gevrey estimates at threshold zero. As application, we establish large time expansions of semigroups e --tH and e --itH for t > 0 with subexponential time-decay estimates on the remainder, including possible presence of zero eigenvalue and real resonances.