Christoph Neuner: Supersingular perturbations of self-adjoint operators with spectrum on the whole real line

Abstract: We will look at perturbations of self-adjoint operators in four cases: the operators are either semibounded or not and the perturbations either singular or supersingular. The case of singular perturbations is well-known. Furthermore, supersingular perturbations of semibounded operators have been described in a Hilbert space model due to Kurasov.
With this background, we will go into the remaining case and answer: is it possible to find a Hilbert space model that interprets the supersingular perturbation of non-semibounded self-adjoint operators and generalizes the model for semibounded operators?
The talk is based on joint work with Annemarie Luger and Pavel Kurasov.