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

*(English. Russian original)*Zbl 1153.35367
St. Petersbg. Math. J. 17, No. 3, 409-433 (2006); translation from Algebra Anal. 17, No. 3, 47-80 (2006).

Summary: 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.

##### MSC:

35P05 | General topics in linear spectral theory for PDEs |

47F05 | General theory of partial differential operators |

35Q40 | PDEs in connection with quantum mechanics |

81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |

35B10 | Periodic solutions to PDEs |

##### Keywords:

generalized periodic Dirac operator; matrix-valued potential; absolutely continuous spectrum
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\textit{L. I. Danilov}, St. Petersbg. Math. J. 17, No. 3, 409--433 (2006; Zbl 1153.35367); translation from Algebra Anal. 17, No. 3, 47--80 (2006)

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