MTP Seminar

Konstantin Merz

(TU Braunschweig)

"Eigenvalue Estimates for Schrödinger Operators Using Fourier Analysis"

Date: Tue, September 21, 2021
Time: 11:45
Place: Room 120 Research I and online via zoom (please write the organizer (s.petrat AT for the meeting id and passcode)

Abstract: Estimating the location and accumulation rate of eigenvalues of Schrödinger operators is a classic problem in spectral theory and mathematical physics. For "short-range" potentials these problems can often be effectively treated using Fourier analytic methods like the Tomas-Stein restriction theorem. As an example we derive eigenvalue asymptotics for Schrödinger-type operators whose kinetic energy vanishes on a codimension one submanifold. Time permitting, we discuss another example: locating eigenvalues of ordinary Schrödinger operators with randomized, long-range, complex-valued potentials using a randomized version of the Tomas-Stein theorem by Bourgain. The talk is based on joint work with Jean-Claude Cuenin.