On Lieb–Thirring inequalities for multidimensional Schrödinger operators with complex potentials

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发表日期：

2025年8月26日

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Sabine Bögli,
Sukrid Petpradittha,
František Štampach

摘要

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 Schrödinger operators in $\mathbb {R}^{d}$ $R^{d}$ to the case of complex-valued potentials. A counter-example has already been found for the one-dimensional case $d=1$ $d = 1$ by the first and third authors in [J. Spectr. Theory 11 (2021), 1391–1413]. Here we generalise the counter-example to higher dimensions $d\ge 2$ $d \geq 2$ .