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...
| Main Authors: | , |
|---|---|
| Format: | Text |
| Language: | unknown |
| Published: |
arXiv
2008
|
| Subjects: | |
| Online Access: | https://dx.doi.org/10.48550/arxiv.0806.1393 https://arxiv.org/abs/0806.1393 |
| _version_ | 1821575380376485888 |
|---|---|
| author | Bruneau, Vincent Ouhabaz, E. -M. |
| author_facet | Bruneau, Vincent Ouhabaz, E. -M. |
| author_sort | Bruneau, Vincent |
| collection | DataCite |
| 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 |
| genre | laptev |
| genre_facet | laptev |
| id | ftdatacite:10.48550/arxiv.0806.1393 |
| institution | Open Polar |
| language | unknown |
| op_collection_id | ftdatacite |
| op_doi | https://doi.org/10.48550/arxiv.0806.1393 https://doi.org/10.1063/1.2969028 |
| 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/ |
| publishDate | 2008 |
| publisher | arXiv |
| record_format | openpolar |
| spelling | ftdatacite:10.48550/arxiv.0806.1393 2025-01-16T22:58:37+00:00 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 |
| 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 |
| title | 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_short | Lieb-Thirring estimates for non self-adjoint Schrödinger operators |
| title_sort | lieb-thirring estimates for non self-adjoint schrödinger operators |
| topic | Spectral Theory math.SP Mathematical Physics math-ph FOS Mathematics FOS Physical sciences |
| topic_facet | Spectral Theory math.SP Mathematical Physics math-ph FOS Mathematics FOS Physical sciences |
| url | https://dx.doi.org/10.48550/arxiv.0806.1393 https://arxiv.org/abs/0806.1393 |