Absolutely continuous spectrum of Dirac systems with potentials infinite at infinity

Source 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.