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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
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