On the discrete eigenvalues of Schrödinger operators with complex potentials

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

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).