Cwikel’s bound reloaded

Spectral Methods in Mathematical Physics

26 February 14:00 - 15:00

Tobias Ried - Max Planck Institute for Mathematics in the Sciences

There are a couple of proofs by now for the famous Cwikel-Lieb-Rozenblum (CLR) inequality, which is a semiclassical bound on the number of bound states for a Schrödinger operator.
In this talk I will show how Cwikel's original approach can be drastically generalised, leading to an astonishingly good bound for the constant in the CLR inequality. Our proof is also quite flexible and leads to rather precise bounds for a large class of Schrödinger-type operators with generalised kinetic energies. Moreover, it highlights a natural but overlooked connection of the CLR bound with bounds for maximal Fourier multipliers from harmonic analysis.
Joint work with D. Hundertmark, P. Kunstmann, S. Vugalter.
Søren Fournais
Aarhus University
Rupert Frank
LMU Munich
Benjamin Schlein
University of Zurich, UZH
Simone Warzel
TU Munich


Rupert Frank


For practical matters at the Institute, send an e-mail to