In this talk I shall present constructions of Schrödinger operators with complex-valued potentials whose spectra exhibit interesting properties. One example shows that for sufficiently large $p$, the discrete eigenvalues need not be bounded in modulus by the $L^p$ norm of the potential. This is a counterexample to the Laptev-Safronov conjecture (Comm. Math. Phys. 2009). Another construction proves optimality (in some sense) of generalisations of Lieb-Thirring inequalities to the non-selfadjoint case - thus giving us information about the accumulation rate of the discrete eigenvalues to the essential spectrum. This talk is based on joint works with Jean-Claude Cuenin (Loughborough) and Frantisek Stampach (Prague).
On the discrete eigenvalues of Schrödinger operators with complex potentials
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Nom de l'orateur
Sabine Boegli
Etablissement de l'orateur
Durham University, UK
Date et heure de l'exposé
Lieu de l'exposé
Salle des séminaires