Gevrey-Type Resolvent Estimates at the Threshold for a Class of Non-Selfadjoint Schrödinger Operators
DOI:
https://doi.org/10.6092/issn.2240-2829/5891Keywords:
Gevrey estimate of resolvent, threshold spectral analysis, non-selfadjoint Schrödinger operators, Witten LaplacianAbstract
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.References
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