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

Danilov, L.

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

Absence of eigenvalues for the generalized two-dimensional periodic Dirac operator
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by L. I. Danilov
Translated by: A. Plotkin

St. Petersburg Math. J. 17 (2006), 409-433

DOI: https://doi.org/10.1090/S1061-0022-06-00911-3

Published electronically: 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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