On Lieb-Thirring inequalities for multidimensional Schrödinger operators with complex potentials
arXiv:2510.02192 · doi:10.1007/s00020-025-02810-0
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 Schrödinger 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.
24 pages