Resolvent estimates and the spectrum of the Dirac operator with periodical potential

Some estimates of the norm of resolvent of Dirac operator on $n$-dimensional tores ($n\ge 2$) for complex values of quasimomentum are given. The absolutely continuity of the spectrum of periodical Dirac operator with potential $V\in L_{\mathrm {\mathrm {loc}}}^\beta (\mathbb R^3)$, $\beta >3$, is proved.