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arXiv · 2510.02192

On Lieb-Thirring inequalities for multidimensional Schr\"odinger operators with complex potentials

Sabine Bögli·Sukrid Petpradittha·František Štampach
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Abstract

We solve the open problem by Demuth, Hansmann, and Katriel announced in [Integr. Equ. Oper. Theory 75 (2013), 1-5] by a counter-example construction. The problem concerns a possible generalisation of the Lieb-Thirring inequality for Schr\"odinger operators in to the case of complex-valued potentials. A counter-example has already been found for the one-dimensional case by the first and third authors in [J. Spectr. Theory 11 (2021), 1391-1413]. Here we generalise the counter-example to higher dimensions.

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Sabine Bögli, Sukrid Petpradittha, František Štampach. 2025-10-02. On Lieb-Thirring inequalities for multidimensional Schr\"odinger operators with complex potentials. https://doi.org/10.1007/s00020-025-02810-0

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