Maha Aafarani
Published 2019-10-07Version 1
We study the large-time behavior of the solutions to the Schr\"odinger equation associated with a non-selfadjoint operator having zero energy eigenvalue and real resonances. Our results extend those of Jensen and Kato in the three-dimensional selfadjoint case. We consider a model of Schr\"odinger operator with a quickly decaying potential in dimension three. We assume that the latter has a finite number of real resonances. We are interested in the expansions of the resolvent in the low energy part and near positive resonances. In particular, we discuss, under different conditions, the three situations of zero energy: zero is an eigenvalue or a resonance, or both.
Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials
Eigenfunction expansions for the Schrödinger equation with inverse-square potential
The $L^{p}-L^{\acute{p}}$ Estimate for the Schrödinger Equation on the Half-Line
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