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

Fischbacher, Christoph, Naboko, Serguei, Wood, Ian (2023) Complete Non-Selfadjointness for Schrödinger Operators on the Semi-Axis. Algebra i Analiz / St. Petersburg Mathematical Journal, 35 (1). pp. 283-303. (Access to this publication is currently restricted. You may be able to access a copy if URLs are provided) (KAR id:99934)

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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.

Item Type: Article
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Funders: University of Kent (https://ror.org/00xkeyj56)
Depositing User: Ian Wood
Date Deposited: 07 Feb 2023 15:04 UTC
Last Modified: 25 Sep 2023 09:33 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/99934 (The current URI for this page, for reference purposes)

University of Kent Author Information

Fischbacher, Christoph.

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Naboko, Serguei.

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Wood, Ian.

Creator's ORCID: https://orcid.org/0000-0001-7181-7075
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