AbstractRead PDF

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

Dominic P. Clemence;Frank Ingram

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.

Received
27/12/2017
, Accepted
05/02/2018
Downloaded
0
, Viewed
0