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.
Key words: Discrete Dirac, ac spectrum, 1-dimensional, Jacobi matrix.
Full Text
Article Information
| Title | On the a.c. spectrum of the 1D discrete Dirac operator |
| Source | Methods Funct. Anal. Topology, Vol. 20 (2014), no. 3, 252-273 |
| MathSciNet |
MR3242707 |
| zbMATH |
1324.47066 |
| Milestones | Received 06/05/2013; Revised 06/02/2014 |
| Copyright | The 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
Citation Example
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.
BibTex
@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 = {http://mfat.imath.kiev.ua/article/?id=696},
}
