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arXiv · 2108.09617

Complete Non-Selfadjointness for Schrödinger Operators on the Semi-Axis

Christoph Fischbacher·Serguei Naboko·Ian Wood
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Abstract

In this note we investigate complete non-selfadjointness for all maximally dissipative extensions of a Schrödinger 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.

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Christoph Fischbacher, Serguei Naboko, Ian Wood. 2022-12-12. Complete Non-Selfadjointness for Schrödinger Operators on the Semi-Axis. https://arxiv.org/abs/2108.09617

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