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

Xue Ping Wang


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.


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

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DOI: 10.6092/issn.2240-2829/5891


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