Theoretical and Mathematical Physics

, Volume 103, Issue 1, pp 349-365

First online:

Resolvent estimates and spectrum of the Dirac operator with periodic potential

  • L. I. DanilovAffiliated withPhysicotechnical Institute of the Ural Division of the Russian Academy of Sciences

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Some estimates are given of the norm of the resolvent of the Dirac operator on ann-dimensional torus (n ≥ 2) for complex values of the quasimomentum. It is shown that the spectrum of the periodic Dirac operator with potential\(V \in L_{loc}^\beta (R^3 ),\beta > 3\), β>3, is absolutely continuous.