St. Petersburg Mathematical Society

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

Author(s): L. I. Danilov
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 17 (2005), vypusk 3.
Journal: St. Petersburg Math. J. 17 (2006), 409-433.
MSC (2000): Primary 35P05
Posted: March 9, 2006
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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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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: 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): 12/JAN/2004
Posted: March 9, 2006
Copyright of article: Copyright 2006, American Mathematical Society

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ISSN: 1547-7371(e) ISSN: 1061-0022(p)

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