Complete Non-Selfadjointness for Schr\"odinger Operators on the Semi-Axis
Spectral Theory
2022-12-14 v3 Functional Analysis
Abstract
In this note we investigate complete non-selfadjointness for all maximally dissipative extensions of a Schr\"odinger operator on a half-line with dissipative bounded potential and dissipative boundary condition. We show that all maximally dissipative extensions that preserve the differential expression are completely non-selfadjoint. However, it is possible for maximally dissipative extensions to have a one-dimensional reducing subspace on which the operator is selfadjoint. We give a characterisation of these extensions and the corresponding subspaces and present a specific example.
Cite
@article{arxiv.2108.09617,
title = {Complete Non-Selfadjointness for Schr\"odinger Operators on the Semi-Axis},
author = {Christoph Fischbacher and Serguei Naboko and Ian Wood},
journal= {arXiv preprint arXiv:2108.09617},
year = {2022}
}
Comments
16 pages, fixed a few mistakes, removed a technical assumption on the imaginary part of the potential $V$