A simple proof of Hardy-Lieb-Thirring inequalities
Rupert L. Frank
TL;DR
This paper presents a concise, unified proof of Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators, covering optimal parameters and establishing a link between magnetic and non-magnetic cases.
Contribution
It provides a simplified, comprehensive proof for Hardy-Lieb-Thirring inequalities and shows that magnetic inequalities follow from non-magnetic ones.
Findings
Proof covers the optimal parameter range.
Establishes that magnetic inequalities follow from non-magnetic ones.
Utilizes a recent inequality by Solovej, Soerensen, and Spitzer.
Abstract
We give a short and unified proof of Hardy-Lieb-Thirring inequalities for moments of eigenvalues of fractional Schroedinger operators. The proof covers the optimal parameter range. It is based on a recent inequality by Solovej, Soerensen, and Spitzer. Moreover, we prove that any non-magnetic Lieb-Thirring inequality implies a magnetic Lieb-Thirring inequality (with possibly a larger constant).
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