# Cwikel estimates and negative eigenvalues of Schrödinger operators on noncommutative tori

@article{Mcdonald2021CwikelEA,
title={Cwikel estimates and negative eigenvalues of Schr{\"o}dinger operators on noncommutative tori},
author={Edward Mcdonald and Raphael Ponge},
journal={Journal of Mathematical Physics},
year={2021}
}
• Published 24 February 2021
• Mathematics
• Journal of Mathematical Physics
In this paper, we establish Cwikel-type estimates for noncommutative tori for any dimension n ≥ 2. We use them to derive Cwikel–Lieb–Rozenblum inequalities and Lieb–Thirring inequalities for negative eigenvalues of fractional Schrödinger operators on noncommutative tori. The latter leads to a Sobolev inequality for noncommutative tori. On the way, we establish a “borderline version” of the abstract Birman–Schwinger principle for the number of negative eigenvalues of relatively compact form…
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