Abstract: In this talk we discuss spectral properties of Schrödinger
operators with delta and delta'-interactions
supported on hypersurfaces, which separate the Euclidean space into finitely
many bounded and unbounded Lipschitz domains.
It turns out that the combinatorial properties of the Lipschitz partition
and the spectral properties
of the corresponding operators are related.
As the main result we present an operator inequality for the Schrödinger
operators with delta and delta'-interactions
which is based on an optimal colouring and involves the chromatic number of
the partition.
This inequality implies various relations for the spectra of the Schrödinger
operators
and it allows to transform known results for Schrödinger operators
with delta-interactions to Schrödinger operators with delta'-interactions.
The talk is based on joint work with Pavel Exner and Vladimir Lotoreichik
