On Lieb–Thirring inequalities for one-dimensional non-self-adjoint Jacobi and Schrödinger operators
Sabine Bögli
Durham University, UKFrantišek Štampach
Czech Technical University in Prague, Czechia
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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 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].
Cite this article
Sabine Bögli, František Štampach, On Lieb–Thirring inequalities for one-dimensional non-self-adjoint Jacobi and Schrödinger operators. J. Spectr. Theory 11 (2021), no. 3, pp. 1391–1413
DOI 10.4171/JST/378