The theory of perturbations for a polyharmonic operator with non-smooth periodic potential

In space $L_2(R^n)$, $n>1$ is considered operator $H_\alpha=(-\Delta)^\ell+\alpha V$, $\alpha\in[-1,1]$, $4\ell>n+1$, $V$ – real, periodical potential. She convergent series of perturbation theory for the eigenfunctions and eigenvalues on the rich set of kvasiimpulse are constructed.