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On real resonances for three-dimensional Schrödinger operators with point interactions

1 Institute for Applied Mathematics, University of Bonn, Endenicher Allee 60, D-53115 Bonn, Germany
2 Gran Sasso Science Institute – GSSI, Viale Francesco Crispi 7, 67100 L’Aquila, Italy

This contribution is part of the Special Issue: Qualitative Analysis and Spectral Theory for Partial Differential Equations
Guest Editor: Veronica Felli
Link: www.aimspress.com/mine/article/5511/special-articles

Special Issues: Qualitative Analysis and Spectral Theory for Partial Differential

We prove the absence of positive real resonances for Schrödinger operators with finitely many point interactions in $\mathbb{R}^3$ and we discuss such a property from the perspective of dispersive and scattering features of the associated Schrodinger propagator.
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Keywords point interactions; singular perturbations of the Laplacian; positive resonances; limiting absorption principle; definite positive functions

Citation: Alessandro Michelangeli, Raffaele Scandone. On real resonances for three-dimensional Schrödinger operators with point interactions. Mathematics in Engineering, 2021, 3(2): 1-14. doi: 10.3934/mine.2021017


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