On Lieb--Thirring inequalities for one-dimensional non-self-adjoint Jacobi and Schr{\" o}dinger operators

Sabine Bögli; František Štampach

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arXiv · 2004.09794

On Lieb--Thirring inequalities for one-dimensional non-self-adjoint Jacobi and Schr{\" o}dinger operators

Sabine Bögli·František Štampach

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Abstract

We study to what extent Lieb--Thirring inequalities are extendable from self-adjoint to general (possibly non-self-adjoint) Jacobi and Schr\"{o}dinger operators. Namely, we prove the conjecture of Hansmann and Katriel from [Complex Anal. Oper. Theory 5, No. 1 (2011), 197-218] and answer another open question raised therein. The results are obtained by means of asymptotic analysis of eigenvalues of discrete Schr\"{o}dinger 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 Schr\"{o}dinger operators with complex-valued potentials published by Demuth, Hansmann, and Katriel in [Integral Equations Operator Theory 75, No. 1 (2013), 1-5].

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Sabine Bögli, František Štampach. 2020-04-21. On Lieb--Thirring inequalities for one-dimensional non-self-adjoint Jacobi and Schr{\" o}dinger operators. https://arxiv.org/abs/2004.09794

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