Ouhabaz: Lieb-Thirring estimates for non-self-adjoint Schr ¨ dinger operators
Abstract. For general non-symmetric operatorsA, we prove that the moment of order γ ≥ 1 of negative real-parts of its eigenval-ues is bounded by the moment of order γ of negative eigenvalues of its symmetric part H = 1 2 [A + A∗]. As an application, we ob-tain Lieb-Thirring estimates for non self-ad...
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| Format: | Text |
| Language: | English |
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| Online Access: | http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.593.8023 http://hal.archives-ouvertes.fr/docs/00/28/62/74/PDF/Lieb-ThirringNSA7.pdf |
| Summary: | Abstract. For general non-symmetric operatorsA, we prove that the moment of order γ ≥ 1 of negative real-parts of its eigenval-ues is bounded by the moment of order γ of negative eigenvalues of its symmetric part H = 1 2 [A + A∗]. As an application, we ob-tain Lieb-Thirring estimates for non self-adjoint Schrödinger oper-ators. In particular, we recover recent results by Frank, Laptev, Lieb and Seiringer [11]. We also discuss moment of resonances of Schrödinger self-adjoint operators. 1. |
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