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

Danilov, L.

doi:10.1090/S1061-0022-06-00911-3

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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
Posted: March 9, 2006
MathSciNet review: 2167843
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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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