On the a.c. spectrum of the 1D discrete Dirac operator

Authors

  • S. Golénia Institut de Mathematiques de Bordeaux Universite Bordeaux 1 351, cours de la Lib'eration F-33405 Talence cedex
  • T. Haugomat Universite de Rennes 1, 263 avenue du Gnral Leclerc CS 74205 - 35042 RENN ´ES CEDEX, Ecole normale sup´ erieure de Cachan Antenne de Bretagne, Campus de Ker Lann Avenue Robert Schuman 35170 Bruz - France

DOI:

Keywords:

Discrete Dirac, ac spectrum, 1-dimensional, Jacobi matrix

Abstract

In this paper, under some integrability condition, we prove that an electrical perturbation of the discrete Dirac operator has purely absolutely continuous spectrum for the one dimensional case. We reduce the problem to a non-self-adjoint Laplacian-like operator by using a spin up/down decomposition and rely on a transfer matrices technique.

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Published

2014-09-25

Issue

Vol. 20 No. 3 (2014)

Section

Articles

How to Cite

Golénia, S., and T. Haugomat. “On the a.c. Spectrum of the 1D Discrete Dirac Operator”. Methods of Functional Analysis and Topology, vol. 20, no. 3, Sept. 2014, pp. 252-73, https://zen.imath.kiev.ua/index.php/mfat/article/view/582.