Lieb-Thirring estimates for non self-adjoint Schrödinger operators
International audience For general non-symmetric operators $A$, we prove that the moment of order $\gamma \ge 1$ of negative real-parts of its eigenvalues is bounded by the moment of order $\gamma$ of negative eigenvalues of its symmetric part $H = \frac{1}{2} [A + A^*].$ As an application, we obtai...
Published in: | Journal of Mathematical Physics |
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Main Authors: | , |
Other Authors: | , |
Format: | Article in Journal/Newspaper |
Language: | English |
Published: |
HAL CCSD
2008
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Subjects: | |
Online Access: | https://hal.archives-ouvertes.fr/hal-00286274 https://hal.archives-ouvertes.fr/hal-00286274/document https://hal.archives-ouvertes.fr/hal-00286274/file/Lieb-ThirringNSA7.pdf https://doi.org/10.1063/1.2969028 |
Summary: | International audience For general non-symmetric operators $A$, we prove that the moment of order $\gamma \ge 1$ of negative real-parts of its eigenvalues is bounded by the moment of order $\gamma$ of negative eigenvalues of its symmetric part $H = \frac{1}{2} [A + A^*].$ As an application, we obtain Lieb-Thirring estimates for non self-adjoint Schrödinger operators. In particular, we recover recent results by Frank, Laptev, Lieb and Seiringer \cite{FLLS}. We also discuss moment of resonances of Schrödinger self-adjoint operators. |
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