AG Mathematische Physik, Dr. Konstantin Merz (Braunschweig): Eigenvalue estimates for Schrödinger operators using Fourier analysis

Dr. Konstantin Merz (Braunschweig)

Eigenvalue estimates for Schrödinger operators using Fourier analysis

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.