Littlewood-Paley decomposition of operator densities and application to a new proof of the Lieb-Thirring inequality

TL;DR

This paper develops a Littlewood-Paley decomposition for operator densities and applies it to provide a new proof of the Lieb-Thirring inequality, enhancing understanding of spectral properties of quantum operators.

Contribution

It introduces a novel Littlewood-Paley decomposition for operator densities and uses it to establish a new proof of the Lieb-Thirring inequality.

Findings

New Littlewood-Paley decomposition for operator densities

A novel proof of the Lieb-Thirring inequality

Enhanced spectral analysis techniques

Abstract

The goal of this note is to prove a analogue of the Littewood-Paley decomposition for densities of operators and to use it in the context of Lieb-Thirring inequalities.