The Asymptotic Behavior of the Titchmarsh-Weyl m-function for a Dirac System on the Line

The Titchmarsh-Weyl matrix m-function for the Dirac equation y 0 =  p (λ +c+v1) (−λ +c+v2) −p  y on the line is shown through analysis of the Jost functions, to be asymptotically diagonal and λ− independent as |λ| → ∞ through complex values. An immediate consequence of this behavior is that the spectral function ρ associated with the equation on the line has an asymptotically diagonal linear form, and hence the absence of large eigen values for the associated operator is confirmed.