Weyl’s Laws and Connes’ Integration Formulas for Matrix-Valued $$L\!\log \!L$$-Orlicz Potentials

@article{Ponge2021WeylsLA,
title={Weyl’s Laws and Connes’ Integration Formulas for Matrix-Valued \$\$L\!\log \!L\$\$-Orlicz Potentials},
author={Raphael Ponge},
journal={Mathematical Physics, Analysis and Geometry},
year={2021}
}
• Raphael Ponge
• Published 28 July 2021
• Mathematics
• Mathematical Physics, Analysis and Geometry
Thanks to the Birman-Schwinger principle, Weyl’s laws for Birman-Schwinger operators yields semiclassical Weyl’s laws for the corresponding Schrödinger operators. In a recent preprint Rozenblum established quite general Weyl’s laws for Birman-Schwinger operators associated with pseudodifferential operators of critical order and potentials that are product of L log L -Orlicz functions and Alfhors-regular measures supported on a submanifold. In this paper, we show that, for matrix-valued L log L…
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