On Lieb-Thirring inequalities for multidimensional Schr\"odinger operators with complex potentials
Spectral Theory
2025-10-03 v1 Mathematical Physics
Analysis of PDEs
math.MP
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.
Cite
@article{arxiv.2510.02192,
title = {On Lieb-Thirring inequalities for multidimensional Schr\"odinger operators with complex potentials},
author = {Sabine Bögli and Sukrid Petpradittha and František Štampach},
journal= {arXiv preprint arXiv:2510.02192},
year = {2025}
}
Comments
24 pages