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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

Absence of eigenvalues for the generalized two-dimensional periodic Dirac operator


Author: L. I. Danilov
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 17 (2005), nomer 3.
Journal: St. Petersburg Math. J. 17 (2006), 409-433
MSC (2000): Primary 35P05
Published electronically: March 9, 2006
MathSciNet review: 2167843
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Abstract | References | Similar Articles | Additional Information

Abstract: A generalized two-dimensional periodic Dirac operator is considered, with $ L^{\infty}$-matrix-valued coefficients of the first-order derivatives and with complex matrix-valued potential. It is proved that if the matrix-valued potential has zero bound relative to the free Dirac operator, then the spectrum of the operator in question contains no eigenvalues.


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Additional Information

L. I. Danilov
Affiliation: Physical-Technical Institute, Ural Branch of the Russian Academy of Sciences, Kirov Street 132, Izhevsk 426000, Russia
Email: danilov@otf.pti.udm.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-06-00911-3
PII: S 1061-0022(06)00911-3
Keywords: Generalized periodic Dirac operator, matrix-valued potential, absolutely continuous spectrum
Received by editor(s): January 12, 2004
Published electronically: March 9, 2006
Article copyright: © Copyright 2006 American Mathematical Society