Cwikel’s bound reloaded
Spectral Methods in Mathematical Physics
06 February 16:00 - 17:00
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)
University of Zurich, UZH