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

Boegli, Sabine; Stampach, Frantisek

doi:10.4171/jst/378

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

Boegli, Sabine; Stampach, Frantisek

Authors

Dr Sabine Boegli sabine.boegli@durham.ac.uk
Associate Professor

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