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

Boegli, Sabine; Stampach, Frantisek

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