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JEAM., Volume(4) - Issue(1), 2018 pp 29-33, http://dx.doi.org/10.18831/djmaths.org/2018011003
The Asymptotic Behavior of the Titchmarsh-Weyl m-function for a Dirac System on the Line
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.
Keywords
Jost function, Dirac equation, Spectral function, Diagonal linear form, Eigen values.