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...
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ftunivnantes:oai:HAL:hal-00286274v1 2023-05-15T17:07:15+02:00 Lieb-Thirring estimates for non self-adjoint Schrödinger operators Bruneau, Vincent Ouhabaz, E.-M. Institut de Mathématiques de Bordeaux (IMB) Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS) 2008 https://hal.science/hal-00286274 https://hal.science/hal-00286274/document https://hal.science/hal-00286274/file/Lieb-ThirringNSA7.pdf https://doi.org/10.1063/1.2969028 en eng HAL CCSD American Institute of Physics (AIP) info:eu-repo/semantics/altIdentifier/arxiv/0806.1393 info:eu-repo/semantics/altIdentifier/doi/10.1063/1.2969028 hal-00286274 https://hal.science/hal-00286274 https://hal.science/hal-00286274/document https://hal.science/hal-00286274/file/Lieb-ThirringNSA7.pdf ARXIV: 0806.1393 doi:10.1063/1.2969028 info:eu-repo/semantics/OpenAccess ISSN: 0022-2488 Journal of Mathematical Physics https://hal.science/hal-00286274 Journal of Mathematical Physics, 2008, 49, pp.093504. ⟨10.1063/1.2969028⟩ [MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP] [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] info:eu-repo/semantics/article Journal articles 2008 ftunivnantes https://doi.org/10.1063/1.2969028 2023-02-08T05:42:35Z 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. Article in Journal/Newspaper laptev Université de Nantes: HAL-UNIV-NANTES Journal of Mathematical Physics 49 9 093504 |
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Université de Nantes: HAL-UNIV-NANTES |
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English |
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[MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP] [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] |
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[MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP] [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] Bruneau, Vincent Ouhabaz, E.-M. Lieb-Thirring estimates for non self-adjoint Schrödinger operators |
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[MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP] [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] |
description |
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. |
author2 |
Institut de Mathématiques de Bordeaux (IMB) Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS) |
format |
Article in Journal/Newspaper |
author |
Bruneau, Vincent Ouhabaz, E.-M. |
author_facet |
Bruneau, Vincent Ouhabaz, E.-M. |
author_sort |
Bruneau, Vincent |
title |
Lieb-Thirring estimates for non self-adjoint Schrödinger operators |
title_short |
Lieb-Thirring estimates for non self-adjoint Schrödinger operators |
title_full |
Lieb-Thirring estimates for non self-adjoint Schrödinger operators |
title_fullStr |
Lieb-Thirring estimates for non self-adjoint Schrödinger operators |
title_full_unstemmed |
Lieb-Thirring estimates for non self-adjoint Schrödinger operators |
title_sort |
lieb-thirring estimates for non self-adjoint schrödinger operators |
publisher |
HAL CCSD |
publishDate |
2008 |
url |
https://hal.science/hal-00286274 https://hal.science/hal-00286274/document https://hal.science/hal-00286274/file/Lieb-ThirringNSA7.pdf https://doi.org/10.1063/1.2969028 |
genre |
laptev |
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laptev |
op_source |
ISSN: 0022-2488 Journal of Mathematical Physics https://hal.science/hal-00286274 Journal of Mathematical Physics, 2008, 49, pp.093504. ⟨10.1063/1.2969028⟩ |
op_relation |
info:eu-repo/semantics/altIdentifier/arxiv/0806.1393 info:eu-repo/semantics/altIdentifier/doi/10.1063/1.2969028 hal-00286274 https://hal.science/hal-00286274 https://hal.science/hal-00286274/document https://hal.science/hal-00286274/file/Lieb-ThirringNSA7.pdf ARXIV: 0806.1393 doi:10.1063/1.2969028 |
op_rights |
info:eu-repo/semantics/OpenAccess |
op_doi |
https://doi.org/10.1063/1.2969028 |
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Journal of Mathematical Physics |
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49 |
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9 |
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093504 |
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1766062610149539840 |