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Research Article

Year : 2018 | Volume: 4 | Issue: 1 | Pages: 29-33

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

Dominic P. Clemence1*, Frank Ingram2

DOI: 10.18831/djmaths.org/2018011003

Corresponding author

Dominic P. Clemence*

Department of Mathematics, North Carolina A&T State University.

  • 1. Department of Mathematics, North Carolina A&T State University.

Received on: 2017/12/27

Revised on: 2018/02/03

Accepted on: 2018/02/05

Published on: 2018/02/09

  • The Asymptotic Behavior of the Titchmarsh-Weyl m-function for a Dirac System on the Line, Dominic P. Clemence, Frank Ingram., 2018/02/09, DJ Journal of Engineering and applied Mathematics. , 4(1): 29-33, http://dx.doi.org/10.18831/djmaths.org/12018011003.

    Published on: 2018/02/09

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.