Research lectures, seminars and events
The events listed in this area are research seminars, workshops and lectures hosted by Durham University departments and research institutes. If you are not a member of the University, but wish to enquire about attending one of the events please contact the organiser or host department.
Analysis and/of PDE: Improved eigenvalue bounds for SchrÃ¶dinger operators with slowly decaying potentials
We extend a result of Davies and Nath  on the location of eigenvalues of SchrÃ¶dinger operators $-\Delta+V$ with slowly decaying complex-valued potentials to higher dimensions. We also discuss examples related to the Laptev--Safronov conjecture , which stipulates that the absolute value of any complex eigenvalue can be bounded in terms of the $L^q$ norm of $V$, for a certain range of exponents $q$. The talk is based on .
 Davies, E. B. and Nath, J. SchrÃ¶dinger operators with slowly decaying potentials J. Comput. Appl. Math., 2002, 148, 1-28
 Laptev, A. and Safronov, O. Eigenvalue estimates for SchrÃ¶dinger operators with complex potentials Comm. Math. Phys., 2009, 292, 29-54
 Cuenin, J.-C. Improved eigenvalue bounds for Schr\"odinger operators with slowly decaying potentials arXiv e-prints, 2019, arXiv:1904.03954
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