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Durham University

Department of Mathematical Sciences

Seminars

This week's seminars

Analysis and/of PDE: Improved eigenvalue bounds for Schrödinger operators with slowly decaying potentials

Presented by Jean-Claude Cuenin, Loughborough

14 November 2019 14:00 in CM301

We extend a result of Davies and Nath [1] on the location of eigenvalues of Schrödinger operators $-\Delta+V$ with slowly decaying complex-valued potentials to higher dimensions. We also discuss examples related to the Laptev--Safronov conjecture [2], 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 [3].

[1] Davies, E. B. and Nath, J. Schrödinger operators with slowly decaying potentials J. Comput. Appl. Math., 2002, 148, 1-28

[2] Laptev, A. and Safronov, O. Eigenvalue estimates for Schrödinger operators with complex potentials Comm. Math. Phys., 2009, 292, 29-54

[3] Cuenin, J.-C. Improved eigenvalue bounds for Schr\"odinger operators with slowly decaying potentials arXiv e-prints, 2019, arXiv:1904.03954

Contact djoko.wirosoetisno@durham.ac.uk for more information

Research Seminars by Series

The research groups in the Department of Mathematical Sciences hold several seminar series in term time. Information on date, time and location are available here.

For information on previous years' seminars please see the seminar archives pages.