Pavel Exner: Spectral estimates for some ‘non-Weyl’ Schrödinger operators

In this talk I am going to discuss spectral estimates for several classes of Schrödinger operators which exhibit a discrete spectrum although the corresponding phase space volume is infi nite. The first concerns the well-known example of narrowing potential channels with the aim to show that the spectrum may be purely discrete even for potentials unbounded from below. Next I will consider Dirichlet Laplacians in cusp-shaped regions and derive inequalities of Lieb-Thirring type showing how they depend on the geometry of the regions, more speci cally on bending or twisting of the cusps. This is a common work with Diana Barseghyan.