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


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.

Key words: Discrete Dirac, ac spectrum, 1-dimensional, Jacobi matrix.

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Article Information

TitleOn the a.c. spectrum of the 1D discrete Dirac operator
SourceMethods Funct. Anal. Topology, Vol. 20 (2014), no. 3, 252-273
MathSciNet   MR3242707
zbMATH 1324.47066
Milestones  Received 06/05/2013; Revised 06/02/2014
CopyrightThe Author(s) 2014 (CC BY-SA)

Authors Information

Sylvain Gol'enia
Institut de Mathematiques de Bordeaux Universite Bordeaux 1 351, cours de la Lib'eration F-33405 Talence cedex

Tristan 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

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Sylvain Golénia and Tristan Haugomat, On the a.c. spectrum of the 1D discrete Dirac operator, Methods Funct. Anal. Topology 20 (2014), no. 3, 252-273.


@article {MFAT696,
    AUTHOR = {Golénia, Sylvain and Haugomat, Tristan},
     TITLE = {On the a.c. spectrum of the 1D discrete Dirac operator},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {20},
      YEAR = {2014},
    NUMBER = {3},
     PAGES = {252-273},
      ISSN = {1029-3531},
  MRNUMBER = {MR3242707},
 ZBLNUMBER = {1324.47066},
       URL = {},

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