Schrödinger operators and singular infinite rank perturbations
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Beschreibung
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.
Autor*in
Christian Kühn
Themen in »Schrödinger operators and singular infinite rank perturbations«
Schrödinger operators singular interactions delta-interactions perturbation theory spectral theory