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Absolutely continuous spectrum of Dirac systems with potentials infinite at infinity

Published online by Cambridge University Press:  01 September 1997

KARL MICHAEL SCHMIDT
KARL MICHAEL SCHMIDT
Affiliation:
Mathematisches Institut der Universität, Theresienstraße 39, D-80333 München, Germany; e-mail: kschmidt@rz.mathematik.uni-muenchen.de
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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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 122 , Issue 2 , September 1997 , pp. 377 - 384
Copyright
Cambridge Philosophical Society 1997

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