Absolutely continuous spectrum of Dirac systems with potentials infinite at infinity

Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024 1997. Absolutely continuous spectrum of Dirac systems with potentials infinite at infinity. Mathematical Proceedings of the Cambridge Philosophical Society 122 (2) , pp. 377-384.

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Abstract

It is shown that the spectrum of a one-dimensional Dirac operator with a potential q tending to infinity at infinity, and such that the positive variation of 1/q is bounded, covers the whole real line and is purely absolutely continuous. An example is given to show that in general, pure absolute continuity is lost if the condition on the positive variation is dropped. The appendix contains a direct proof for the special case of subordinacy theory used.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Additional Information:	Pdf uploaded in accordance with publisher's policy at http://www.sherpa.ac.uk/romeo/issn/0305-0041/ (accessed 25/02/2014).
Publisher:	Cambridge University Press
ISSN:	0305-0041
Date of First Compliant Deposit:	30 March 2016
Last Modified:	06 May 2023 02:15
URI:	https://orca.cardiff.ac.uk/id/eprint/26482

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