Yu. Karpeshina
On Spectral Properties of Periodic Polyharmonic Matrix Operators.
(501K, postscript)
ABSTRACT. We consider a matrix operator $H=(-\Delta )^l+ V
$ in $R^n$, where $n\geq 2$, $l\geq 1$, $4l>n+1$, and $V$ is the
operator of multiplication by a periodic in $x$ matrix $V(x)$. We
study spectral properties of $H$ in the high energy region.
Asymptotic formulae for Bloch eigenvalues and the corresponding
spectral projections are constructed. The Bethe-Sommerfeld
conjecture, stating that the spectrum of $H$ can have only a
finite number of gaps, is proved.