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

#### Abstract

*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

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DOI: 10.6092/issn.2240-2829/5891

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