Counting bound states with maximal Fourier multipliers

Dirk Hundertmark; Peer Christian Kunstmann; Tobias Ried; Semjon Vugalter

doi:10.4171/ecr/18

BooksecrCollected Volumepp. 197–207

Counting bound states with maximal Fourier multipliers

Dirk Hundertmark
Karlsruhe Institute of Technology (KIT), Germany; University of Illinois at Urbana-Champaign, USA
- MathSciNet
- zbMATH Open
Peer Christian Kunstmann
Karlsruher Institut für Technologie (KIT), Germany
- MathSciNet
- zbMATH Open
Tobias Ried
Max-Planck Institut für Mathematik in den Naturwissenschaften, Leipzig, Germany
Semjon Vugalter
Karlsruhe Institute of Technology (KIT), Germany

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Abstract

We report on a version of Cwikel’s proof of the famous Cwikel–Lieb–Rozenblum (CLR) inequality which highlights the connection of the CLR inequality to maximal Fourier multipliers. This new approach enables us to get a constant at least ten times better than Cwikels in all dimensions. In dimensions $d \geq 5$ our results are better than all previously known ones.