Abstract

The Titchmarsh-Weyl matrix m-function for the Dirac equation on the line is shown, through analysis of the Jost functions, to be asymptotically diagonal and independent of the spectral parameter as it becomes infinite through complex values. An immediate consequence of this behavior is that the spectral function associated with the equation on the line has an asymptotically diagonal linear form, and hence the absence of large eigenvalues for the associated operator.