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

Boegli, Sabine; Stampach, Frantisek

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


Authors

Frantisek Stampach



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].

Citation

Boegli, S., & Stampach, F. (2021). On Lieb-Thirring inequalities for one-dimensional non-self-adjoint Jacobi and Schrödinger operators. Journal of Spectral Theory, 11(3), 1391-1413. https://doi.org/10.4171/jst/378

Journal Article Type Article
Acceptance Date Jul 22, 2020
Online Publication Date Sep 30, 2021
Publication Date 2021
Deposit Date Nov 13, 2020
Publicly Available Date Oct 27, 2022
Journal Journal of Spectral Theory
Print ISSN 1664-039X
Publisher EMS Press
Peer Reviewed Peer Reviewed
Volume 11
Issue 3
Pages 1391-1413
DOI https://doi.org/10.4171/jst/378

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