Lieb-Thirring estimates for non self-adjoint Schrödinger operators

For general non-symmetric operators $A$, we prove that the moment of order $γ\ge 1$ of negative real-parts of its eigenvalues is bounded by the moment of order $γ$ of negative eigenvalues of its symmetric part $H = {1/2} [A + A^*].$ As an application, we obtain Lieb-Thirring estimates for non self-a...

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Main Authors: Bruneau, Vincent, Ouhabaz, E. -M.
Format: Text
Language:unknown
Published: arXiv 2008
Subjects:
Spectral Theory math.SP
Mathematical Physics math-ph
FOS Mathematics
FOS Physical sciences
laptev
Online Access:https://dx.doi.org/10.48550/arxiv.0806.1393
https://arxiv.org/abs/0806.1393
id ftdatacite:10.48550/arxiv.0806.1393
record_format openpolar
spelling ftdatacite:10.48550/arxiv.0806.1393 2023-05-15T17:07:15+02:00 Lieb-Thirring estimates for non self-adjoint Schrödinger operators Bruneau, Vincent Ouhabaz, E. -M. 2008 https://dx.doi.org/10.48550/arxiv.0806.1393 https://arxiv.org/abs/0806.1393 unknown arXiv https://dx.doi.org/10.1063/1.2969028 arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Spectral Theory math.SP Mathematical Physics math-ph FOS Mathematics FOS Physical sciences article-journal Article ScholarlyArticle Text 2008 ftdatacite https://doi.org/10.48550/arxiv.0806.1393 https://doi.org/10.1063/1.2969028 2022-04-01T15:18:57Z For general non-symmetric operators $A$, we prove that the moment of order $γ\ge 1$ of negative real-parts of its eigenvalues is bounded by the moment of order $γ$ of negative eigenvalues of its symmetric part $H = {1/2} [A + A^*].$ 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. Text laptev DataCite Metadata Store (German National Library of Science and Technology)
institution Open Polar
collection DataCite Metadata Store (German National Library of Science and Technology)
op_collection_id ftdatacite
language unknown
topic Spectral Theory math.SP
Mathematical Physics math-ph
FOS Mathematics
FOS Physical sciences
spellingShingle Spectral Theory math.SP
Mathematical Physics math-ph
FOS Mathematics
FOS Physical sciences
Bruneau, Vincent
Ouhabaz, E. -M.
Lieb-Thirring estimates for non self-adjoint Schrödinger operators
topic_facet Spectral Theory math.SP
Mathematical Physics math-ph
FOS Mathematics
FOS Physical sciences
description For general non-symmetric operators $A$, we prove that the moment of order $γ\ge 1$ of negative real-parts of its eigenvalues is bounded by the moment of order $γ$ of negative eigenvalues of its symmetric part $H = {1/2} [A + A^*].$ 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.
format Text
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 arXiv
publishDate 2008
url https://dx.doi.org/10.48550/arxiv.0806.1393
https://arxiv.org/abs/0806.1393
genre laptev
genre_facet laptev
op_relation https://dx.doi.org/10.1063/1.2969028
op_rights arXiv.org perpetual, non-exclusive license
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
op_doi https://doi.org/10.48550/arxiv.0806.1393
https://doi.org/10.1063/1.2969028
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