Counting bound states with maximal Fourier multipliers

  • Dirk Hundertmark

    Karlsruhe Institute of Technology (KIT), Germany; University of Illinois at Urbana-Champaign, USA
  • Peer Christian Kunstmann

    Karlsruher Institut für Technologie (KIT), Germany
  • Tobias Ried

    Max-Planck Institut für Mathematik in den Naturwissenschaften, Leipzig, Germany
  • Semjon Vugalter

    Karlsruhe 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.