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On Lieb-Thirring inequalities for one-dimensional non-self-adjoint Jacobi and Schrödinger operators

Boegli, Sabine and Stampach, Frantisek (2021) 'On Lieb-Thirring inequalities for one-dimensional non-self-adjoint Jacobi and Schrödinger operators.', Journal of spectral theory., 11 (3). pp. 1391-1413.

Abstract

We study to what extent Lieb–Thirring inequalities are extendable from self-adjoint to general (possibly non-self-adjoint) Jacobi and Schrödinger operators. Namely, we prove the conjecture of Hansmann and Katriel from [12] and answer another open question raised therein. The results are obtained by means of asymptotic analysis of eigenvalues of discrete Schrödinger operators with rectangular barrier potential and complex coupling. Applying the ideas in the continuous setting, we also solve a similar open problem for one-dimensional Schrödinger operators with complex-valued potentials published by Demuth, Hansmann, and Katriel in [5].

Item Type:Article
Full text:Publisher-imposed embargo
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.4171/jst/378
Publisher statement:© 2021 European Mathematical Society Published by EMS Press This work is licensed under a CC BY 4.0 license.
Date accepted:22 July 2020
Date deposited:13 November 2020
Date of first online publication:30 September 2021
Date first made open access:27 October 2022

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