Counting bound states with maximal Fourier multipliers
Dirk HundertmarkKarlsruhe Institute of Technology (KIT), Germany; University of Illinois at Urbana-Champaign, USA
Peer Christian KunstmannKarlsruher Institut für Technologie (KIT), Germany
Tobias RiedMax-Planck Institut für Mathematik in den Naturwissenschaften, Leipzig, Germany
Semjon VugalterKarlsruhe Institute of Technology (KIT), Germany
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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 our results are better than all previously known ones.