The present thesis consist of two parts. The abstract part is concerned
with singular infinite rank perturbations of selfadjoint operators.
Starting with a selfadjoint operator we construct a chain of rigged
Hilbert spaces and investigate some of their properties. Afterwards this
operator is perturbed by another operator whose range is contained in
one of the rigged Hilbert spaces with negative index. The rigorous
definition of such a perturbation is done with the help of ordinary and
generalized boundary triples. Hereby we have to distinguish different
cases, depending on the index mentioned above.
Using this abstract
approach we consider in the second part of this thesis Schrödinger
operators with delta-interactions supported on manifolds, give criteria
for selfadjointness and investigate their spectra. Also here we have to
distinguish different cases, depending on the codimension of the
manifold. Special attention is paid to the case that the manifold has
codimension two, in particular to the case of a closed curve in the
three-dimensional Euclidean space.