Abstract
We improve the Lieb–Thirring type inequalities by Demuth, Hansmann and Katriel (J. Funct. Anal. 2009) for Schrödinger operators with complex-valued potentials. Our result involves a positive, integrable function. We show that in the one-dimensional case the result is sharp in the sense that if we take a non-integrable function, then an analogous inequality cannot hold.
Dedicated to the memory of Sergey Naboko
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Acknowledgements
The author is grateful for the comments of the anonymous referee, and thanks Jean-Claude Cuenin, Rupert L. Frank, František Štampach and Alexei Stepanenko for helpful discussions.
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Bögli, S. (2023). Improved Lieb–Thirring Type Inequalities for Non-selfadjoint Schrödinger Operators. In: Brown, M., et al. From Complex Analysis to Operator Theory: A Panorama. Operator Theory: Advances and Applications, vol 291. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-31139-0_9
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DOI: https://doi.org/10.1007/978-3-031-31139-0_9
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